Is it possible to retrieve app's local data after uninstalling it?
Answer 1

The usual practice for games backing up users' progress online is storing almost everything on the company's own private server, while storing a small "identity" file on device (much like Cookies in a browser), or use device's identifier / your Play Games identity directly. The company's employees (not all of them, but at least the development and support teams) have access to their storage.

Answer 2

Continuing Answer 1, there's no way for you to prove that you're the owner of the deleted profile, and the company don't want to get into trouble if you claim another player's profile. This is a bad practice because (probably) the game does not use device identifier.

Answer 3

As GiantTree has already pointed out in comments, you should check out this post.