Make sure you have the Google Play Games app installed. If you see the Google Play popup when booting up Vampire Survivors it is working and will automatically upload your save to the cloud.
If it doesn't pop up on Android, please make sure you do the following:
1) Check you have the Google Play Games app installed
2) Check that you have your Google Account linked correctly by going to “Settings” at the top right, and clicking on “Change account for games” at the bottom under “Your data”
This should show you Vampire Survivors and which account you have linked to the game.