Push Notification -didFinishLaunchingWithOptions

Since you only want to present a viewController when you get a Push Notification, you may try utilizing NSNotificationCenter for your purposes:

Part 1: Set up a class (in your case, the rootViewController) to listen/respond to a NSNotification

Suppose, MainMenuViewController is the rootViewController of your navigationController.
Set up this class to listen to a NSNotification:

- (void)viewDidLoad {
    //...
    [[NSNotificationCenter defaultCenter] addObserver:self
                                             selector:@selector(presentMyViewOnPushNotification)
                                                 name:@"HAS_PUSH_NOTIFICATION"
                                               object:nil];
}

-(void)presentMyViewOnPushNotification {
    //The following code is no longer in AppDelegate
    //it should be in the rootViewController class (or wherever you want)

    UIStoryboard *mainstoryboard = [UIStoryboard storyboardWithName:@"MainStoryboard" bundle:nil];
    PushMessagesVc *pvc = [mainstoryboard instantiateViewControllerWithIdentifier:@"PushMessagesVc"];

    [self presentViewController:pvc animated:YES completion:nil];
    //either presentViewController (above) or pushViewController (below)
    //[self.navigationController pushViewController:pvc animated:YES];
}

---

Part 2: Post Notification (possible from anywhere in your code)

In your case, AppDelegate.m methods should look like:

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions {
    //firstly, don't sleep the thread, it's pointless
    //sleep(1); //remove this line

    if (launchOptions) { //launchOptions is not nil
        NSDictionary *userInfo = [launchOptions valueForKey:UIApplicationLaunchOptionsRemoteNotificationKey];
        NSDictionary *apsInfo = [userInfo objectForKey:@"aps"];

        if (apsInfo) { //apsInfo is not nil
            [self performSelector:@selector(postNotificationToPresentPushMessagesVC) 
                       withObject:nil
                       afterDelay:1];
        }
    }
    return YES;
}

-(void)application:(UIApplication *)application didReceiveRemoteNotification:(NSDictionary *)userInfo {
    //this method can be done using the notification as well
    [self postNotificationToPresentPushMessagesVC];
}

-(void)postNotificationToPresentPushMessagesVC {
    [[NSNotificationCenter defaultCenter] postNotificationName:@"HAS_PUSH_NOTIFICATION" object:nil];
}

---

PS: I haven’t done this for my projects (yet) but it works and is the best way i could think of doing this kinda stuff (for the moment)