If you had your computer all the way shut off, nothing can start it, except for a human being pushing on the power button.
If Windows was in the process of installing an update, it would not have shut down all of the way. Updates often do restarts.
The other possibility is that your computer was hibernating or sleeping and not shut down. If that were the case, just about anything might start your computer (including a power surge). Most likely it was not a hacker.