This is what cookies were invented for. It could easily save her progress in a persistent cookie with no need to sign up. (Signing up might still be an optiona

This is what cookies were invented for. It could easily save her progress in a persistent cookie with no need to sign up. (Signing up might still be an optional way of persisting that state beyond the cookie, for example to share progress between cookies, but that could easily come later and only when the user wants it)