but what is the earliest plausible date for an assault rifle and what is the earliest plausible date for mass adoption by any nation?
well, the op technically covers the bar and Chauchat, but that's not in the spirit of things
and i think that the maxim patents start dropping of in 1902-1905, so that helps
but i think that it's unlikely to see a major military adopting anything prior to ww1, and only then as rear line/expedient weapon
formal adoption may be possible in 1938 if a design can fill the requirements of the light rifle contract
but having said that, revolutionary, paramilitary, and law enforcement might be more open to the idea,
ex.
china was under an arms embargo as of 1919, they might see a "light automatic rifle" as a way around that as "it's totally not an lmg, we swear" sort of thing
the us- mexican border conflict of the 1910's saw a number of us states fielding ranger companies, many prominent members of those companies had served in the spanish- american war and might be open to the idea
the fbi in the 1920's/30's purchased a number of colt monitors as well as thompson smgs and winchester/remington auto carbines, the right bit of prodding might push them towards a single rifle to replace the others