New house. Ventilation conduits under the floor make a bong/bong noise
when a person walks across the floor. How can one eliminate this
sound? Seems to recede on cold days when vent conduits carry warm air
and return on warm days when air conditioning directs cool air through
the system.

Is there a crawl space? Can some one near the ducts in order to "tune" them?

A bit of insulation between the floor and the duct might work.  Sound
like a trial and error job for a patient handyman.

The ductwork is not properly supported.  I am a home inspector with
TMK Inspections.  You can visit us at www.tmkinspections.com.  There
are codes that the builder/sub-contractor should have followed to
properly install the ducts.  These can be obtained for your state
registrar of contactors.  I work out of Scottsdale, Arizona.  Our
state publishes a minimum requirement for builders that can be viewed
online.  First, go back to your builder and they should fix it.  If
that does not work call your registrar and file a complaint.  They
will get you some satisfaction.  Good Luck.