What I would do is look at the documentation around taking over the display. Many of the examples also take over the display too, so it's easy to work out how to do it.
Once you have control of the display you can call any function on the display yourself, but you should only do so in the rendering callback or instance of CustomDrawing that you provide to the renderer.
Both the OO - CustomDrawing and functional - renderingCallback methods are fully documented here, and again can be found in many examples. In the examples we usually make the menu take back over when the button is pressed, but you could also detect any change in the rotary encoder too, so then any button would wake it up. Of course, you could also do it many different ways as well, but I think this would be easiest.
Documentation for take over display:
https://www.thecoderscorner.com/products/arduino-libraries/tc-menu/renderer-take-over-display/
Also take a look at the examples, EG:
https://github.com/davetcc/tcMenuLib/blob/6b049aaa2e9ad4c8a3035280c28185aa812c892b/examples/takeOverDisplay/takeOverDisplay.ino#L191