"Gun belts with belt loops existed before 1900, but they were uncommon because at the end of the Civil War there were very few cartridge guns, so there were no cartridges to put into the belt loops."
So, there was a blank in the 35 year period between 1865 (the end of the Civil War) and 1900? Hawg made a good point in this regards, tho Colt was making cartridge revolvers from 1872 on, and Smith&Wesson was making their single action top break .44's from about 1868. The Army had cartridge breech loaders from the Civil War (Spencers in particular, and they were used on the western frontier for several years afterwards), and in 1866 the Trapdoor Springfield was being used, in 58 rimfire, then 50-70, then 45-70 in 1873. The commercial firearms market also was rapidly developing in cartridge guns in the early 1870's. Historically, and from period photgraphs, we know cartridge belts were fairly common in that period, and in the military from the mid-late 1860's.
"Far better it is to dare mighty things, to win glorious triumphs even though checkered by failure, than to rank with those poor spirits who neither enjoy nor suffer much because they live in the gray twilight that knows neither victory nor defeat." -Theodore Roosevelt-