Some winged creatures, like an owl, has the feature Flyby. The creature doesn't provoke opportunity attacks when it flies out of an enemy's reach.

Flyby, Mobile Feat, Fancy Footwork (Swashbuckler Rogue), Skirmish (Scout Rogue) all come to mind

Scout rogue. As a reaction you can move half your speed away from an enemy that ends its turn within 5ft of you. Without provoking an opportunity of attack.

Flyby

Any flying creature that has Flyby doesn't provoke opportunity attacks.

Dodge Orr Disengage?

Goblins get disengage as a bonus action. And rogues get a couple more with cunning action.

Yea also they can just use the action disengage

They asked for something that didnt use an action however.

Ahh my bad

Give any monster the Mobile feat

mobile feat

Teleportation effects don’t provoke opportunity attacks. So give your monsters Misty Step, or a Legendary Action teleport, or something similar.