I think that:

Privacy best practice is to know nothing, or as little as possible, about the user.

If storing progress is required, and local device storage is not sufficient, a minimalist online setup is the desirable solution.

An automatically generated user id and a simple user-progress table should be enough. GCloud has all the required parts ready to go.

In any case this whole thing should come after the user has had a chance to experience the product.

But that’s just me.

I ain’t no power-to-be ;)