@ 08:48 am (GMT)
Thomas Kitchenhi Charles welcome to the forum.
the Answer is in the question WIDELY ADOPTED.
the 7.92x33 and the sturmgewehr 44 was very late in ww2 yes you could class it as the first but not widely adopted, i don't think the cartridge itself made it very far as its very mild.
MP 43, MP 44, StG 44
Grenadiers operating in the area of Aachen, Germany in 1944
As work moved forward to incorporate this new firing system, development halted when Hitler suspended all new rifle programs due to administrative infighting within the Third Reich. Hitler ordered that newer submachine guns were to be built, and he strongly disagreed with the use of the Kurz ammunition. To keep the MKb 42(H) development program alive, the Waffenamt (Armament Office) re-designated the weapon as the Maschinenpistole 43 (MP 43) and, making a few improvements, billed the weapon as an upgrade to existing submachine guns.
Much time was wasted trying to make the MP 43 a replacement for the Karabiner 98k rifle. This goal was eventually realized to be impossible; the MP 43 cartridge was too weak to fire rifle grenades, too inaccurate for sniping, and the weapon was too short for bayonet fighting. In September 1943, it was decided that the MP 43 would supplement rather than replace the Kar 98k. As a result, the optical sight base, grenade-launching extended muzzle thread, and bayonet lug were removed.
Adolf Hitler eventually discovered the designation deception and halted the program again. In March 1943, he permitted it to recommence for evaluation purposes only. Running for six months until September 1943, the evaluation produced positive results, and Hitler allowed the MP 43 program to continue in order to make mass production possible. The first MP 43s were distributed to the Waffen-SS; in October 1943, some were issued to the 93rd Infantry Division on the Eastern Front. Production and distribution continued to different units. In April 1944, Hitler took some interest in the weapon tests and ordered the weapon (with some minor updates) to be re-designated as the MP 44. In July 1944, at a meeting of the various army heads about the Eastern Front, when Hitler asked what they needed, a general exclaimed, "More of these new rifles!". The exclamation caused some confusion (Hitler's response is reputed to have been "What new rifle?"), but once Hitler saw the MP 44 being demonstrated, he was impressed and gave it the title Sturmgewehr. Seeing the possibility of a propaganda gain, the rifle was again renamed as the Sturmgewehr 44 (StG 44), to highlight the new class of weapon it represented. The designation translates to "Assault rifle, model 1944", thereby introducing the term "assault rifle".