If you are going for the scenario of an incoming call, it's not the same for both platforms.
For Android, you can start an activity responding to a push notification, but iOS doesn't allow that. You can either send a regular push notification the user might miss, or use CallKit and integrate it with your stuffs.
Unfortunately I don't know good libraries for React Native that can help you with that yet, so it might have to be done natively and bridged to your RN code.
Edit:
Android example - In your native code handling a notification, you can use context.startActivity(launchIntent); to launch your app with an incoming call screen.