I used Facebook login to identify users. When a new user comes, I store their userID in my database. Next time they come, I recognized their Facebook ID and I know which use
Altough JWTs can be validated locally with the public key, (Google APIs Client Library downloads and caches they public keys automatically) checking the token on Google's side via the https://www.googleapis.com/oauth2/v1/tokeninfo endpoint is necessary to check if the access for the applicaton has been revoked since the creation of the token.