MaterialApp widget is not rebuilding even though it is wraped with a consumer widget

Question

I am trying to navigate to two different screens dynamically by using a ternary operator in the initialRoute of my material app but I am able to authenticate but does not update the current auth screen to my home screen. Below is the code for my materialApp widget.

Consumer<Auth>(
        builder: (context, authData, _) => MaterialApp(
          debugShowCheckedModeBanner: false,
          title: 'Cinema',
          theme: ThemeData(brightness: Brightness.dark),
          initialRoute:
              authData.isAuth ? HomeScreen.routName : AuthScreen.routeName,
          routes: {
            AuthScreen.routeName: (context) => AuthScreen(),
            HomeScreen.routName: (context) => const HomeScreen(),
            MovieDetailScreen.routeName: (context) => const MovieDetailScreen(),
            FavoriteMovies.routName: (context) => const FavoriteMovies(),
          },
        ),
      ),

Below is the code of the auth where I check whether my token is true is false That is there is a token or not.

class Auth with ChangeNotifier {
  String? _token;
  DateTime? _expiryDate;
  String? _userId;

  bool get isAuth {
    return token != null;
  }

  String? get token {
    if (_token != null &&
        _expiryDate != null &&
        _expiryDate!.isAfter(DateTime.now())) {
      return _token;
    }
    return null;
  }

  Future<void> authenticate(
      String email, String password, String urlSegment) async {
    const _apiKey = '*******************************';
    final url =
        'https://identitytoolkit.googleapis.com/v1/accounts:$urlSegment?key=$_apiKey';
    try {
      final response = await http.post(
        Uri.parse(url),
        body: json.encode(
          {
            'email': email,
            'password': password,
            'returnSecureToken': true,
          },
        ),
      );
      final responseData = json.decode(response.body);
      if (responseData['error'] != null) {
        throw HttpException(responseData['error']['message']);
      }
      _token = responseData['idToken'];
      _userId = responseData['localId'];
      _expiryDate = DateTime.now().add(
        Duration(
          seconds: int.parse(
            responseData['expiresIn'],
          ),
        ),
      );
      print(isAuth); // This prints true whenever I call this authenticate method
      notifyListeners();
    } catch (error) {
      print(error);
    }
  }
}