FirebaseMessaging.instance.getInitialMessage() is not called in terminated state

Given that you not displayed how you setup your fcm , here is how to go about it

/// Create a [AndroidNotificationChannel] for heads up notifications
late AndroidNotificationChannel channel;

/// Initialize the [FlutterLocalNotificationsPlugin] package.
late FlutterLocalNotificationsPlugin flutterLocalNotificationsPlugin;

/// To verify things are working, check out the native platform logs.
Future<void> firebaseMessagingBackgroundHandler(RemoteMessage message) async {
  // If you're going to use other Firebase services in the background, such as Firestore,
  // make sure you call `initializeApp` before using other Firebase services.
  await Firebase.initializeApp(
    options: DefaultFirebaseOptions.currentPlatform,
  );
  print('Handling a background message ${message.messageId}');
}

in main.dart

WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp(
    options: DefaultFirebaseOptions.currentPlatform,
  );
  FirebaseMessaging.onBackgroundMessage(firebaseMessagingBackgroundHandler);


// setup displaying notifications 

channel = const AndroidNotificationChannel(
      'high_importance_channel', // id
      'High Importance Notifications', // title// description
      importance: Importance.high,
    );

    flutterLocalNotificationsPlugin = FlutterLocalNotificationsPlugin();

    /// Create an Android Notification Channel.
    ///
    /// We use this channel in the `AndroidManifest.xml` file to override the
    /// default FCM channel to enable heads up notifications.
    await flutterLocalNotificationsPlugin
        .resolvePlatformSpecificImplementation<
            AndroidFlutterLocalNotificationsPlugin>()
        ?.createNotificationChannel(channel);

    /// Update the iOS foreground notification presentation options to allow
    /// heads up notifications.
    await FirebaseMessaging.instance
        .setForegroundNotificationPresentationOptions(
      alert: true,
      badge: true,
      sound: true,
    );

handle message call this in your initstate

FirebaseMessaging.instance
        .getInitialMessage()
        .then((RemoteMessage? message) {
      if (message != null) {
        // do message things
      }
    });
    FirebaseMessaging.onMessageOpenedApp.listen((RemoteMessage message) {
      showMessage(message: message);
    });
    FirebaseMessaging.onMessage.listen((RemoteMessage message) {
      RemoteNotification? notification = message.notification;
      AndroidNotification? android = message.notification?.android;

      if (notification != null && android != null) {
        flutterLocalNotificationsPlugin.show(
            notification.hashCode,
            notification.title,
            notification.body,
            NotificationDetails(
                android: AndroidNotificationDetails(
                  channel.id,
                  channel.name,
                ),
                iOS: IOSNotificationDetails(subtitle: notification.title)));
      }
    });

incase you need to navigate on receiving a message

void showMessage({required RemoteMessage message}) async {
    if (message.data['route'] == "mypage") {
      var myparams =  message.data['payload'];
      Navigator.of(context).push(MaterialPageRoute(
          fullscreenDialog: true,
          builder: (_) {
            return MyPage(
             params:myparams,
            );
          })); ...

With FCM, you can send two types of messages to clients:

• Notification messages, are sometimes thought of as "display messages." These are handled by the FCM SDK automatically.
• Data messages, which are handled by the client app. "

https://firebase.google.com/docs/cloud-messaging/concept-options

What you are trying to send is a data message, my best guess is that the firebase SDK does not recognize the data message so it does not trigger the firebase message event listener. Your notification must have a 'notification' field for firebase SDK to listen to.