In Flutter FireBase google sign how to maintain persistence sign for my given code

I my project I am using google sign in and i want to maintain persistent sign in how to do it for the below code. The problem is once i sign in and if i close the app then when I reopen the app i have to sign in again.

Once I open the app i get an option to Sign in with google once i sign in with google I got to the first screen where details about me the signed in user are available and then if i close the app without signing in then when I restart the application i have to sign in again how should i sign in once and be signed in until i press the sign out button

main.dart

    import 'package:flutter/material.dart';

    import 'login_page.dart';

    void main() => runApp(MyApp());

    class MyApp extends StatelessWidget {
      @override
      Widget build(BuildContext context) {
        return MaterialApp(
          debugShowCheckedModeBanner: false,
          title: 'Flutter Login',
          theme: ThemeData(
            primarySwatch: Colors.blue,
          ),
          home: LoginPage(),
        );
      }
    }

login_page.dart

import 'package:chat/sign_in.dart';
    import 'package:flutter/material.dart';

    import 'first_screen.dart';

    class LoginPage extends StatefulWidget {
      @override
      _LoginPageState createState() => _LoginPageState();
    }

    class _LoginPageState extends State<LoginPage> {
      @override
      Widget build(BuildContext context) {
        return Scaffold(
          body: Container(
            color: Colors.white,
            child: Center(
              child: Column(
                mainAxisSize: MainAxisSize.max,
                mainAxisAlignment: MainAxisAlignment.center,
                children: <Widget>[
                  FlutterLogo(size: 150),
                  SizedBox(height: 50),
                  _signInButton(),
                ],
              ),
            ),
          ),
        );
      }

      Widget _signInButton() {
        return OutlineButton(
          splashColor: Colors.grey,
          onPressed: () {
            signInWithGoogle().whenComplete(
              () {
                Navigator.of(context).push(
                  MaterialPageRoute(
                    builder: (context) {
                      return FirstScreen();
                    },
                  ),
                );
              },
            );
          },
          shape: RoundedRectangleBorder(borderRadius: BorderRadius.circular(40)),
          highlightElevation: 0,
          borderSide: BorderSide(color: Colors.grey),
          child: Padding(
            padding: const EdgeInsets.fromLTRB(0, 10, 0, 10),
            child: Row(
              mainAxisSize: MainAxisSize.min,
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                Image(image: AssetImage("assets/google_logo.png"), height: 35.0),
                Padding(
                  padding: const EdgeInsets.only(left: 10),
                  child: Text(
                    'Sign in with Google',
                    style: TextStyle(
                      fontSize: 20,
                      color: Colors.grey,
                    ),
                  ),
                )
              ],
            ),
          ),
        );
      }
    }

sign_in.dart

import 'package:firebase_auth/firebase_auth.dart';
import 'package:google_sign_in/google_sign_in.dart';

final FirebaseAuth _auth = FirebaseAuth.instance;
final GoogleSignIn googleSignIn = GoogleSignIn();

String name;
String email;
String imageUrl;
Future<String> signInWithGoogle() async {
  final GoogleSignInAccount googleSignInAccount = await googleSignIn.signIn();
  final GoogleSignInAuthentication googleSignInAuthentication =
      await googleSignInAccount.authentication;

  final AuthCredential credential = GoogleAuthProvider.getCredential(
    accessToken: googleSignInAuthentication.accessToken,
    idToken: googleSignInAuthentication.idToken,
  );

  final AuthResult authResult = await _auth.signInWithCredential(credential);
  final FirebaseUser user = authResult.user;

  // Checking if email and name is null
  assert(user.email != null);
  assert(user.displayName != null);
  assert(user.photoUrl != null);

  name = user.displayName;
  email = user.email;
  imageUrl = user.photoUrl;

  // Only taking the first part of the name, i.e., First Name
  if (name.contains(" ")) {
    name = name.substring(0, name.indexOf(" "),);
  }

  assert(!user.isAnonymous);
  assert(await user.getIdToken() != null);

  final FirebaseUser currentUser = await _auth.currentUser();
  assert(user.uid == currentUser.uid);

  return 'signInWithGoogle succeeded: $user';
}

void signOutGoogle() async {
  await googleSignIn.signOut();

  print("User Sign Out");
}

first_screen.dart

import 'package:chat/login_page.dart';
import 'package:chat/sign_in.dart';
import 'package:flutter/material.dart';

class FirstScreen extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
        decoration: BoxDecoration(
          gradient: LinearGradient(
            begin: Alignment.topRight,
            end: Alignment.bottomLeft,
            colors: [Colors.blue[100], Colors.blue[400]],
          ),
        ),
        child: Center(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            mainAxisSize: MainAxisSize.max,
            children: <Widget>[
              CircleAvatar(
                backgroundImage: NetworkImage(
                  imageUrl,
                ),
                radius: 60,
                backgroundColor: Colors.transparent,
              ),
              SizedBox(height: 40),
              Text(
                'NAME',
                style: TextStyle(
                    fontSize: 15,
                    fontWeight: FontWeight.bold,
                    color: Colors.black54),
              ),
              Text(
                name,
                style: TextStyle(
                    fontSize: 25,
                    color: Colors.deepPurple,
                    fontWeight: FontWeight.bold),
              ),
              SizedBox(height: 20),
              Text(
                'EMAIL',
                style: TextStyle(
                    fontSize: 15,
                    fontWeight: FontWeight.bold,
                    color: Colors.black54),
              ),
              Text(
                email,
                style: TextStyle(
                    fontSize: 25,
                    color: Colors.deepPurple,
                    fontWeight: FontWeight.bold),
              ),
              SizedBox(height: 40),
              RaisedButton(
                onPressed: () {
                  signInWithGoogle();
                  Navigator.of(context).pushAndRemoveUntil(
                    MaterialPageRoute(
                      builder: (context) {
                        return LoginPage();
                      },
                    ),
                    ModalRoute.withName('/'),
                  );
                },
                color: Colors.deepPurple,
                child: Padding(
                  padding: const EdgeInsets.all(8.0),
                  child: Text(
                    'Sign Out',
                    style: TextStyle(fontSize: 25, color: Colors.white),
                  ),
                ),
                elevation: 5,
                shape: RoundedRectangleBorder(
                    borderRadius: BorderRadius.circular(40)),
              )
            ],
          ),
        ),
      ),
    );
  }
}