Since the serial number is on the firearm, and Buds does not open the Boxes/cases, you'll have to wait until the transfer is done by your FFL and you actually take possession of it.

Hi David and welcome. You normally won't get the serial number until the transfer happens at your local FFL Dealer. You don't technically own the gun until then. You can contact Buds customer Service with your order number to see if they can assist you at 1-859-368-0371 9am-7pm EST Mon-Fri. or use the Blue Chat now button at the bottom right corner 9am to 8pm Mon - Sat and 9am to 7pm Sunday.