Get Touch Event on entire screen

To elaborate @Nicholas Chong advice, here is the example that works for me fine. You can use onTouchStart and onTouchEnd handlers on any View via props:

<View
  onTouchStart={() => doSomething()}
  style={{ width: '100%', height: '100%' }}
/>

More information

onResponderGrant not working for me, and I use onTouchEnd to trigger when tap the screen, this will work

You do not need to warp it with Touchable component.

Add next props to root View.

onResponderGrant - make View handle touch

onStartShouldSetResponder - make View handle start