Check if your BIOS has feature called
PWR-ON After PWR-Fail or something similar. Turn it on.
These features allow you to control what the board does when it receives power. Possible values usually include:
- Power On, as soon as power is received
- Power On, if the device was powered on when the power went off
- Stay Off
The specific settings differs depending on what BIOS is used.
Some boards will respect this setting only if there was an actual power failure (and not if you correctly shut down the machine). Others will apply this setting in either case. And some (especially server) boards even offer both options.