Currently, I am working on the application where user able to login with Google. As part of the login process, we need to send Google ACCESS TOKEN and REFRESH TOKEN to serve
You should use the server auth code flow via Auth.GOOGLE_SIGN_IN_API: get an server auth code on Android client, send to your server, server exchanges the code for refresh and access token (with a secret). There are more details in this blog post as well.
Also, if you are using GoogleAuthUtil.getToken for access token now, you do want to check out this Google Sign-In best practice blog post to see how to migrate to the recommended flow to ensure security and best UX.