Dad will need to file a 709 gift tax return.

Nope.  Gifts aren't taxable to the kid opening up the present from mom and dad.

And mom will also want to file that gift tax return along with dad.

Be aware that for purposes of reporting the sale price and for the son's Basis in the property, in most cases the amount you use is the cost AFTER the so-called "gift of equity".  So if the contract says $330,000 with a "gift of equity" of $66,000, the actual sales price for tax purposes is $264,000 (and that is the Basis of the son too).

In the event that $264,000 is lower than the parents' Basis or if Gift Tax was paid, that can alter things, but that is not common.

Some questions from paid tax preparers make me run for rcooleys fireball...

You should have been visiting here for as long as I have --------------------- you would never leave his Fireball.😲

Is son married?  Did wife join in purchase?  Mom and Dad can give son and wife $64,000 in 2022 with no 709 required, or $68,000 if this happened in 2023.  By the way, what is the penalty for not filing the Form 709?