Explain Google Sign in flow for separate forntend and backend apps

I am working on a NestJS and React app. App should have only google login.

After many hours of searching through awful google docs and web tutorials I am considering the following flow:

1. react stores JWT token obtained via Google Sign In (@react-oauth/google)
   1. a) send additional request from FE to BE to verify token and create user if he does not exist
2. with each request we send that ID_TOKEN to the API,
3. NestJS creates a middleware/guard which verifies every request by using OAuthClient and verifying the token.
4. if token is verified user is considered logged in.
5. if id_token is not valid we send not logged in status code and redirect user to login page

Does this flow make sense?
I am wondering if I need to store some unique data like sub in our db?
Do i need to generate my own JWT?

This will be only login method for now.