I have been using Gmail through iOS 10.3.3's native mail app and I removed the account yesterday. I tried setting up the account again today and no luck. I've tried Google, Exchange, and Other; none work. Did Apple and/or Google change server settings that would prevent me from signing in? When I use the Google default setup, I enter my email > then Password > 2FA code > and the iOS screen goes immediately back to the email choice screen. I have done this several times with the same results. I would prefer to NOT use a third party iOS app for Gmail.