Blanket Procurement shotguns have the US "P" proof marking on the barrel and next door on the receiever. There is a serial number on the barrel that is visible when removed from the receiver. It should match the number on the front flat of the trigger guard assembly. Your gun has no number which means the assembly may be a replacement from a later gun that had the serial number located elsewhere. The feds consider the numbered triggerguard assembly as the "receiver." The missing p is questionable.

BP guns were taken as received, a few rounds fired, the p punch added and in some cases, the U.S. and issued. I have examples with the ps and no us marks. Springfield Research used to have a monograph on the Blank Procurements. Agents were told to purchase only 12 and 16 guage guns but I have a 20 gauge Stevens that made it through the process. Most "advanced" collectors ignore this area of collecting---which I do appreciate.