Best design to let user know about hidden Navigation Drawer

My Android app has a parent screen that has ham menu icon on top left that indicates that user can access Nav Drawer.Parent has multiple child screens. When user navigates down through the child screens, app shows the Nav Up button (left arrow on top left) to indicate that he can navigate up. All good.

I lately realised that the Nav Drawer is accessible even from child screens while they show Nav Up button. And I see it's the same behaviour with most of the Android applications including gmail. In the below gmail screen, the Nav Drawer is accessible though it has nav up button.Even Stackoverflow app has this behaviour.

I added some events to see if users are aware of Nav Drawer accessibility from child screens. Waited 2 weeks, I did not find a single user who knew it and accessed Nav Drawer from child screen that has Nav Up button.

But I want users to know that because there are few valid choices in my app's Nav Drawer that he can make being in the child screens.

  1. What is the best design to indicate users the same ?
  2. What do you think of removing the Nav Up button in child screens and instead show the ham menu icon instead. In this case users can still navigate up with phone back button. Does this sound okay?

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