Hello! I suggest doing this:
1) Determine which variables are involved in "the game state" (score, character position, level, etc) and saving them to a file.
2) Upload the file to the cloud server (you'll tell me why you selected the services you've selected)
3) Use the user session to access their data and download and decode the file.
Does it make sense?
About me: I'm an expert Unity developer. I've designed, built and deploy multiple unity mobile apps -specially AR/VR- for diverse industries. I'm kinda new on freelancer but feel free to check my profile and portfolio. I work hard and clean so you'll love working with me ;)