How to create user in user pool using social identity provider?

I want to login with social identity provider (Google) and after successful authentication , I need to pass Google Auth Token to Cognito User pool to create new user in it. Is it possible? If yes, How can we achieve it?

I think below are steps

1. Login with Google and get Google Auth Token
2. Send it to AWS Cognito User pool to create user

Ref, I went through

https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-pools-identity-federation.html

https://docs.amazonaws.cn/en_us/cognito/latest/developerguide/cognito-user-pools-social-idp.html

https://docs.aws.amazon.com/cognito/latest/developerguide/google.html

https://docs.aws.amazon.com/cognito/latest/developerguide/amazon-cognito-integrating-user-pools-with-identity-pools.html

https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-scenarios.html

https://aws-amplify.github.io/docs/android/authentication

https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-pools-social-idp.html

https://docs.aws.amazon.com/cognito/latest/developerguide/tutorial-integrating-user-pools-android.html