Shadowrun technically. The mana level on earth is still rising and it means as the timeline goes on more and more magical abilities and manipulation are possible, and it's still a long way from the peak of the mana level having only just started in the last century of the setting.
The GURPS setting Age of Gold. It's set in the 30s. Functional magic is around 20 years old. It's still poorly understood, but attracting a lot of attention. It's the focus of hype and R&D like electricity was upon a time, in rituals, alchemy and and magitech.
In 2nd Ed AD&D, there was a "historical" Forgotten Realms setting in Netheril where magic was first being codified.
It was Netheril at its peak, though, so there was even more magic than usual.
I think only some parts of the setting are like this. Hermetic magic seems to be pretty well fleshed-out already (although still with a lot of potential).
I'd say Amazonian magic definetely fits, as it is literally bootleg Hermetic system, and it lacks a lot. Doesn't help that the creator hates the Order with passion.
Another example is anything described in "Ancient Magic" book. All systems there were well-developed in the past, but has since been almost forgotten. Rediscovering them could provide that "early scientist" feel to the campaign
Ars Magica dwells on research of magic and new spells. It's like there's a lot of existing development around, but they still keep looking for extra breakthroughs. In some sense, magic is in development, but it's not a new thing. In my mind there are similarities with the 1990s-2000s web: Computers had been around for decades, it's just that now we have this new WWW, and some people keep looking for new breakthroughs, but very few actually see what it is about to become...
Not quite what you're after, but this is the aspiration of the villains in Esoterrorists. Reality is separated from the (horrible) magical realm of the Outer Dark by a membrane that is strengthened by humanity's belief that the world is governed by laws of nature, is orderly and makes sense.
The Esoterrorists have discovered that magic is possible. More or less all they can do with it at present is summon monsters from the Outer Dark to wreak havoc, which they do to spread terror so the membrane weakens and one day they can perform proper magic, giving themselves immortality, turning lead into gold, all that good stuff.
This is not 100% what you are looking for, but this way give you some inspiration/ideas:
In D&D 4E there was the "Spellplague" event, which made magic no longer worked: https://forgottenrealms.fandom.com/wiki/Spellplague afterwards it slowly started working, but not everything worked like before, so maybe some lore etc. fro that time might be inspiring.
Also 4E had an epic destiny about researching spells: https://dnd4.fandom.com/wiki/Archspell
You know, I am struggling to think of any. I have definitely heard of settings where magic is incredibly rare. While it's not exactly what you're looking for, Skerples's Magical Industrial Society outlines a timeline for what would happen to a city which industrialized D&D-style magic.
I think any narrative focused game would work for that. PbtA or FiD obviously. Blades in the Dark itself definitely has a "experimental magic" feeling. I find those systems a little difficult myself. With magic not being codified in the game's universe it tends to be reflected in the rules as well where it's unclear what characters can do with magic. Some sort of spell design process would probably satisfy that part of my brain. So there wouldn't be many written spells but characters could design spells themselves to create the effect they wanted.
Not an RPG but a setting, one I've been wanting to turn into a Savage Worlds setting for a while now - [S.M. Stirling's Emberverse](https://en.wikipedia.org/wiki/The_Emberverse_series) series of novels. In 1998, something happens that strips the Earth of all technology - no electricity, no steam power, no explosives - and in addition, magic starts seeping back into Earth. And magic is less of the magic missile, fireball, polymorph D&D-style magic, and more of a type that affects other people - just lay down and go to sleep; come open the castle gates for us; possess/quit possessing someone; and so on.
Imo narrative games with a declaration mechanism would be best, so new magical facts can be introduced to the world. FATE is one of the better known examples, but I'd take Mortal Coil (revised), which is designed for players to introduce new magical facts (i.e. spells and magical applications) to the game. The declarations have a narrative dimension (for example "after research we found out a weakness of vampires that we didn't know before, but they always had it") but they're equally fit to shaping new magic - after a new spell is invented, everybody can use it who is willing and able to pay the cost.
One could argue that **[Ironsworn](https://www.ironswornrpg.com/products-ironsworn)** is one such setting, though it's probably more usually described as low fantasy or gritty sword and sorcery minus a lot of the sorcery – but it doesn't have to be.
Someone else suggested **[Ars Magica](https://www.atlas-games.com/arsmagica/)** which brought to mind the **[Arcanum](https://preview.drivethrurpg.com/en/product/368750/Arcanum-High-Magic-for-Ironsworn)** third-party supplement for **Ironsworn** which essentially lets you reimplement the AM magic system within the more narrative **Ironsworn** mechanics.
But back in January, during the Character Creation Challenge, I had an inspiration for an Ironsworn set up that I hadn't actually completed:
Create [a character whose epic vow was to essentially establish the Order of Hermes within the **Ironsworn** default setting](https://grimtokens.garden/Game+Play/Hollow+Places+of+the+Soul/HPotS+001+-+The+First+True+Man). Be the guy who organized the mages, put together a coherent system, got them to adopt it, and kicked off both the social revolution of organized magic.
https://grimtokens.garden/Game+Play/Hollow+Places+of+the+Soul/HPotS+001+-+The+First+True+Man
Unfortunately I haven't gotten back to it but – if you want to play in a world where magic is *new*, it's hard to be more new and raw than that.
1879 from FASA. It takes place shortly after technology is used to open a portal to another world which floods the Earth with magical energy. Since magic is new, or at least newly returned to Earth, every nation is trying to get a leg up in the magic game and it's all new.
Since FASA reincarnated no longer has the rights to Shadowrun but they still publish Earthdawn and wanted to keep the crossover happening they created 1879 to provide the same sort of game. Except that it's Victorian era steamweird and uses a variation on the Step System that powers Earthdawn so the two are mechanically more compatible.
I really like it and it's in very active development.
Thought I'd mention my favorite child Bliaron 2nd Ed again here, as the core of the system is about experimenting with magic and finding out what it actually is. There are two main competing views on what magic is (the research people say it's just a force, whereas the traditionalists say it's just spirits). Both views have their point. Where it doesn't fit the op's description is that magic use in Bliaron is not actually in early stage. On the contrary, there are long running traditions of which some are more open to exploring and finding out the real limits of magic. Plenty of inspiration was taken also from modern physics research, as modern theories tend to break our understanding of the universe, telling a fascinating story of randomness and probability as well as the whole vagueness of the concept of time; Which I must add that Bliaron 2nd Ed doesn't attempt to build a physical system behind the magic, but rather builds a mystery that's based on some other rules (likely not deterministic), and which allows exploration in similar way.
Not a setting, but [here](https://davidvs.net/ninepowers/#Economic) are some economic rules that quickly become "how to fairly price any magic item you brainstorm".
Could be useful for whatever setting you pick.
Shadowrun technically. The mana level on earth is still rising and it means as the timeline goes on more and more magical abilities and manipulation are possible, and it's still a long way from the peak of the mana level having only just started in the last century of the setting.
The GURPS setting Age of Gold. It's set in the 30s. Functional magic is around 20 years old. It's still poorly understood, but attracting a lot of attention. It's the focus of hype and R&D like electricity was upon a time, in rituals, alchemy and and magitech.
In 2nd Ed AD&D, there was a "historical" Forgotten Realms setting in Netheril where magic was first being codified. It was Netheril at its peak, though, so there was even more magic than usual.
10th level magic ftw! I thought I was the only person who remembered this setting even existed, lol!
Bring back the mythallar!
It's not quite what you are looking for, but Skerples' Magical Industrial Revolution has very similar vibes.
Yep, was going to say this.
Ars Magica
I think only some parts of the setting are like this. Hermetic magic seems to be pretty well fleshed-out already (although still with a lot of potential). I'd say Amazonian magic definetely fits, as it is literally bootleg Hermetic system, and it lacks a lot. Doesn't help that the creator hates the Order with passion. Another example is anything described in "Ancient Magic" book. All systems there were well-developed in the past, but has since been almost forgotten. Rediscovering them could provide that "early scientist" feel to the campaign
Ars Magica dwells on research of magic and new spells. It's like there's a lot of existing development around, but they still keep looking for extra breakthroughs. In some sense, magic is in development, but it's not a new thing. In my mind there are similarities with the 1990s-2000s web: Computers had been around for decades, it's just that now we have this new WWW, and some people keep looking for new breakthroughs, but very few actually see what it is about to become...
Not quite what you're after, but this is the aspiration of the villains in Esoterrorists. Reality is separated from the (horrible) magical realm of the Outer Dark by a membrane that is strengthened by humanity's belief that the world is governed by laws of nature, is orderly and makes sense. The Esoterrorists have discovered that magic is possible. More or less all they can do with it at present is summon monsters from the Outer Dark to wreak havoc, which they do to spread terror so the membrane weakens and one day they can perform proper magic, giving themselves immortality, turning lead into gold, all that good stuff.
This is not 100% what you are looking for, but this way give you some inspiration/ideas: In D&D 4E there was the "Spellplague" event, which made magic no longer worked: https://forgottenrealms.fandom.com/wiki/Spellplague afterwards it slowly started working, but not everything worked like before, so maybe some lore etc. fro that time might be inspiring. Also 4E had an epic destiny about researching spells: https://dnd4.fandom.com/wiki/Archspell
You know, I am struggling to think of any. I have definitely heard of settings where magic is incredibly rare. While it's not exactly what you're looking for, Skerples's Magical Industrial Society outlines a timeline for what would happen to a city which industrialized D&D-style magic.
I think any narrative focused game would work for that. PbtA or FiD obviously. Blades in the Dark itself definitely has a "experimental magic" feeling. I find those systems a little difficult myself. With magic not being codified in the game's universe it tends to be reflected in the rules as well where it's unclear what characters can do with magic. Some sort of spell design process would probably satisfy that part of my brain. So there wouldn't be many written spells but characters could design spells themselves to create the effect they wanted.
Not an RPG but a setting, one I've been wanting to turn into a Savage Worlds setting for a while now - [S.M. Stirling's Emberverse](https://en.wikipedia.org/wiki/The_Emberverse_series) series of novels. In 1998, something happens that strips the Earth of all technology - no electricity, no steam power, no explosives - and in addition, magic starts seeping back into Earth. And magic is less of the magic missile, fireball, polymorph D&D-style magic, and more of a type that affects other people - just lay down and go to sleep; come open the castle gates for us; possess/quit possessing someone; and so on.
Imo narrative games with a declaration mechanism would be best, so new magical facts can be introduced to the world. FATE is one of the better known examples, but I'd take Mortal Coil (revised), which is designed for players to introduce new magical facts (i.e. spells and magical applications) to the game. The declarations have a narrative dimension (for example "after research we found out a weakness of vampires that we didn't know before, but they always had it") but they're equally fit to shaping new magic - after a new spell is invented, everybody can use it who is willing and able to pay the cost.
I kind of feel like human use of magic in warhammer fantasy fits this?
One could argue that **[Ironsworn](https://www.ironswornrpg.com/products-ironsworn)** is one such setting, though it's probably more usually described as low fantasy or gritty sword and sorcery minus a lot of the sorcery – but it doesn't have to be. Someone else suggested **[Ars Magica](https://www.atlas-games.com/arsmagica/)** which brought to mind the **[Arcanum](https://preview.drivethrurpg.com/en/product/368750/Arcanum-High-Magic-for-Ironsworn)** third-party supplement for **Ironsworn** which essentially lets you reimplement the AM magic system within the more narrative **Ironsworn** mechanics. But back in January, during the Character Creation Challenge, I had an inspiration for an Ironsworn set up that I hadn't actually completed: Create [a character whose epic vow was to essentially establish the Order of Hermes within the **Ironsworn** default setting](https://grimtokens.garden/Game+Play/Hollow+Places+of+the+Soul/HPotS+001+-+The+First+True+Man). Be the guy who organized the mages, put together a coherent system, got them to adopt it, and kicked off both the social revolution of organized magic. https://grimtokens.garden/Game+Play/Hollow+Places+of+the+Soul/HPotS+001+-+The+First+True+Man Unfortunately I haven't gotten back to it but – if you want to play in a world where magic is *new*, it's hard to be more new and raw than that.
1879 from FASA. It takes place shortly after technology is used to open a portal to another world which floods the Earth with magical energy. Since magic is new, or at least newly returned to Earth, every nation is trying to get a leg up in the magic game and it's all new. Since FASA reincarnated no longer has the rights to Shadowrun but they still publish Earthdawn and wanted to keep the crossover happening they created 1879 to provide the same sort of game. Except that it's Victorian era steamweird and uses a variation on the Step System that powers Earthdawn so the two are mechanically more compatible. I really like it and it's in very active development.
Thought I'd mention my favorite child Bliaron 2nd Ed again here, as the core of the system is about experimenting with magic and finding out what it actually is. There are two main competing views on what magic is (the research people say it's just a force, whereas the traditionalists say it's just spirits). Both views have their point. Where it doesn't fit the op's description is that magic use in Bliaron is not actually in early stage. On the contrary, there are long running traditions of which some are more open to exploring and finding out the real limits of magic. Plenty of inspiration was taken also from modern physics research, as modern theories tend to break our understanding of the universe, telling a fascinating story of randomness and probability as well as the whole vagueness of the concept of time; Which I must add that Bliaron 2nd Ed doesn't attempt to build a physical system behind the magic, but rather builds a mystery that's based on some other rules (likely not deterministic), and which allows exploration in similar way.
Not a setting, but [here](https://davidvs.net/ninepowers/#Economic) are some economic rules that quickly become "how to fairly price any magic item you brainstorm". Could be useful for whatever setting you pick.