I'd like to control my air-purifier with one of those power-socket-timer-switch thingies – Is there a way to "auto-press" those non-mechanical buttons?

This is a Levoit Vital 100 and it has a timer to switch itself off after x hours but i'd like to turn it on automatically.

I'm somewhat fit with soldering and taking stuff apart but i don't wanna go that route before i have atleast a rough understanding of what's up with those buttons.

Thx! 🙂