Obtain a
Solid State Relay having output rating of 10A @ 240 VAC, with 5VDC-24VDC control inputs.
Connect the control input DC output terminals of your USB 3.0 port (observing correct polarity.
Connect the load side of the Solid State Relay:
One terminal to AC Mains "Line".
Other terminal to monitor AC adapter "Line" contact.
Connect monitor AC adapter "Neutral" contact to AC Mains "Neutral".
Use safe and correct wiring methods and supplies to accomplish all of the above.
Now, every time you turn on your computer, the Solid State Relay will be switched on via the 5VDC that appears at your USB 3.0 port, and will switch on your monitor for you.
If your monitor has a soft power switch, you will need to press that to activate the monitor, because most monitors default to a quiescent state when power is applied to them.
Otherwise, leave your monitor on, and let it go into a sleep state when it loses video input from your computer when you turn the computer off.