My son’s account was set up with trainer club. Tab did a software update overnight that logged him out. Trainer club wouldn't accept password so he selected the Google login option but it wants to create a new character. Will he lose all his progress if we move forward? We restarted the tab but the Pokémon app is still in the midst of picking a new character and doesn't give us the trainer account option.
Characters and progress are tied to accounts, so if your son wants to hold onto his, he should log in with the Pokemon Trainer Club as before.
If the app isn't doing this even after a restart, the best option is probably to uninstall the app and download it again from the Google Play store. This won't harm his progress.
All the game data is stored on server side, you can log in and out with as many accounts/game progresses as you wish from the same device and everything will keep working fine. When you logged in with a google account you loaded a new (empty) profile and game progress in which nothing had been done yet. As soon as you log in with your old account again, the old game progress will be restored. This feature also allowes to keep the game progress if you buy a new device or want to play on a device of a friend.
If sometimes the login fails with a message like "Authentification failed. Please try again." repeatedly, don't panic, it's probably just the Pokemon Go servers being down again. Wait a few hours or until the next day and they'll be working again.