Shared subscription, how to start new game without deleting other data

I’ve created an iCloud and game centre account for a child using my Apple Arcade subscription so that they can play a game that I also play. Anytime the app is opened on phone, it is reloaded with the same saved as another device. How do I keep my game saved and start a new game for them to play on the other device? The Apple ID and Game Center are already changed, will resetting the game delete from the same subscription?