You can add the view of the UINavigationController to the UIWindow and either let it obscure the first view or remove that view from the UIWindow. The navigationController won't have a back button to take you back to the first view (since it's stack doesn't include the first controller), so you'll need a custom button if you want to provide a way back.
- (IBAction) buttonPressed {
myNavigationController = [[UINavigationController alloc] initWithRootViewController:mySecondViewController];
[self.view.window addSubview:myNavigationController.view];
[self.view removeFromSuperview];
}
That's the direct answer to your question, however, if you simply want UINavigationController functionality but don't want to see the UINavigationBar on the first screen - check out:
http://stackoverflow.com/questions/1298892/hiding-the-uinavigationbar-only-for-the-root-uiviewcontroller