Will Godzilla have a post credits scene leading something in future sequels?

Judging from Gareth Edwards' dislike of post-credits scenes, I am doubtful. If there is, Gareth'll handle it in a way we've probably never seen.

Perhaps there will be a scene during the ending of the film, not after the credits, that may ask a question. That's my guess.

Gareth said he doesn't like them and the film would feel finished after this movie, so I doubt it

Gareth confirmed in a recent interview that there will be no "buttons" or "stingers". 

I hope so.

we'll have to see