Is there an attic that's accessible? Can he just climb up there and look around?

You didn't take any photos of electrical, plumbing and other systems before the sheetrock went on?

One tool would be a ladder to do what MSO suggested. Another tool would be a hammer to make the access into the attic to do what MSO suggested.

If the HVAC contractor installed a metal supply boot, you may be able to locate it with a stud finder. The task of finding it should fall to your builder.

Use an infrared thermometer with the furnace running. You can easily locate the supplies with it.

After my heat pump runs for awhile, the drywall that hides the supply ducts warms up. Maybe just run the HVAC for awhile, stand on a ladder, and feel the ceiling to see if its warmer in some places than others.

You may be able to use an infra-red thermometer but it requires that warm air can flow along the duct to get to the end of the duct (which is sealed and blocking airflow)! It may work but you might be better off with a metal detector to detect the metal boot at the end of the duct (if you are sure there is a duct behind the drywall).

Assuming the duct is metal...

The duct need not be metal, just the boot. It would be typical in our area.