If smokeless powder was already invented then and machines to help make rimfire cartridges, could a sub/light machine gun be invented?
Of course it could. One could argue if someone didn't had such idea at that point. The main drawbacks were, probably:
- repetition in creation (so what industrialization bring)
- real need to kill many people at once.
First submachine appeared during first World War. With almost 10 millions army men dead. For example Russian-Japanese war had "just" around 1,2 millions participants on each side. Italo-Turkish war had 40 thousands participants on each side.
There was just no need for such kind of weapon to be supplied with money for R&D, materials or building whole infrastructure around it.