The Fedorov Avtomat is possibly the first (see comments) an early firearm used in action that would classify as a true self-loading battle rifle.
It weights in at about 4.4kg compared to the 7.7-8.8kg of the BAR: much closer in weight to that of a battle rifle (rather than a light machine gun).
3200 were produced and it saw action during the Russian civil war and WWII.