flutterfire_ui_auth.dart

import 'package:flutter/material.dart';
import 'package:firebase_core/firebase_core.dart';
import 'package:firebase_auth/firebase_auth.dart';
import 'package:flutterfire_ui/auth.dart';
import 'firebase_options.dart';

Future<void> main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp(options: DefaultFirebaseOptions.currentPlatform);
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) => MaterialApp(
        home: AuthenticationGate(),
      );
}

class AuthenticationGate extends StatelessWidget {
  const AuthenticationGate({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) => StreamBuilder<User?>(
        stream: FirebaseAuth.instance.authStateChanges(),
        builder: (context, snapshot) {
          // User is not signed in - show a sign-in screen
          if (!snapshot.hasData) {
            return SignInScreen(
              providerConfigs: [
                EmailProviderConfiguration(),
                GoogleProviderConfiguration(
                  clientId: 'xxxx-xxxx.apps.googleusercontent.com',
                ),
              ],
            );
          }

          return HomePage(); // show your app’s home page after login
        },
      );
}

Check out the flutterfire_ui plugin and it's support for Google Sign-in: https://firebase.flutter.dev/docs/ui/auth/configuring-providers#google