Can a device turn on by itself Can a device turn on by itself without any buttons being pressed? Assume there aren't any custom ROMs
Yes.

Even stock ROMs have a feature named Scheduled Power-On. 

Phones have a built-in battery to allow RTC (real time clock) to run while the device is powered off, and it's the base that scheduled power-on is designed.

Here's Settings -> Advanced -> Scheduled Power On/Off on my phone (OnePlus 5, Stock 7.1.1)


(click image to enlarge)