I thought 7.62x39 was developed slightly before the Kurz...
I thought it was made for the SKS and then later adopted to the AK based on the success of the Kurz. I could be wrong though.
Also, I must point out that, while not originally an assault cartridge, the 7.62x25 was employed with great success in the Eastern Front by both sides, primarily using the PPSh-style of weaponry to propell it. Though it started as a pistol round, it's performance is most definitely more along the lines of a carbine round, with some of that surplus going as high as even 1900 feet per second. It was in use starting in 1941 at least, and maybe earlier as an assualt round.