"To refer to the original question again concerning cheap, mass-produced blowback operated weapons, when would you say the first one of those actually appeared? The Sten gun? MP-40? PPSH-41? I don't think anything much earlier than about 1940 qualified as cheap and mass-produced, blowback or otherwise. Mass-produced does not also imply cheap, either."
Well, in the handgun world, in the 1890s with Browning's guns.
In the submachine gun world, really the middle to late 1930s and 1940s, and the ones you mention are certainly contenders.
It's odd that, while some designers were designing guns that could be made quickly and cheaply through stampings, welding, and riveting with VERY few machining operations, others were still hard at work designing guns that were massively difficult and time consuming to manufacture.
Probably, though, the Sten would be among the first of the truly "job shop" weapons, which could be largely manufactured with a drill press, a hand operated stamping press, and a welder.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.