dadX3, that Win. 1905 looks like the oldest centerfire semi-auto rifle that used detachable mags available in a higher-than-needed-for-hunting capacity, sold to the general public. It used either 5 or 10 round mags. It might fit the definition of "assault rifle" due to that feature, even though it's basically a deer rifle, with a full length barrel.
That Remington Model 8 only had 5 round mags for the civilian market, but in the 1930s a law enforcement special production model had longer mags that held 10 or 20 rounds. I don't think that was meant to be sold to the public, and even if it "could be" purchased by the public, pretty much no individuals ever bought that rifle with those mags.
Back then there was no 'civilian market', you could buy whatever the manufacturers made just like the Thompsons and Monitors. They also used medium power cartridges, not full power rifle cartridges, similar to 'assault rifles' not using their forbearers high power cartridges(30-06, 8MM, and 7.62x54).
I think the 2 models I listed above were often used by Police and Feds, including in the take-down of Bonnie and Clyde, and other gangsters.