It depends on the timeline in the Indy universe. The P38 used in "Last Crusade" didn't start reaching the troops until 1939. In the same movie, the bad guys are using MP-40s, which only started to appear in 1941. However, the weapon also appeared in "Raiders", which took place in 1935/36, if I remember correctly.
If it happened at 11AM instead of 11PM, it would have been far worse. Even so, I'm reminded of Cannoneer No.4's tagline, I've lost turret power; I have my nods and my .50. Hooah. I will stay until relieved. White 2 out.