I can't give it to Sam Colt. He was a good at marketing and the revolver predated him by centuries. He came along just when the machinery was advanced enough to produce revolvers in large quantities. It's more of a triumph of the industrial revolution than to Sam Colt's genius.
If we use the Browning standard, then it would have to be Garand. Self trained machinist. He wasn't as prolific as Browning but then again he worked to meet gubmint design standards. Like Browning, he was handy in the tool room and when he was told that it would take 2 years to gear up and make the jigs & fixtures to assemble the Garand, John Garand scoffed and went to the tool room and did it himself for 6 months. He didn't profit from his inventions because he was a patriot (and a Canadian to boot).
I'd give Kalashnikov a lot of credit too, but his designs weren't the first. Federov came out with the first gun that really qualified as an "assault gun." The Germans followed with the Stgw44. Kalashnikov took a lot of excellent ideas and combined them into an outstanding package. He deserves a lot of credit for making one of the best military guns of his time (much like Mauser does for the bolt action 98).
Maxim ranks up there but wasn't as prolific as Browning. Methinks he had more medical training (like Gatling) did than mechanical but being open minded, took the advice of one American who suggested that he find a wind to help the Europeans cut each other's throats faster. Maxim = Vickers = Sothrun, essentially all the same machinegun that chewed up an entire generation of young men.
I'm hesitant to put Eugene Stoner up there too. He was also clever in using the gas impingment system (something the French thought up before WW I). However, the versatility of the Stoner Weapon System as manifested in the AR-15 goes to the tinkerers who made it into a SMG, to the target shooters who built space guns and not to Stoner.
Gaston Glock is kinda like Kalashnikov. He took a bunch of good ideas and put them into a working package. He then had a good marketing team make it one of the premier police pistols of this country. However, design wise, the Glock has nothing new as polymers were used before (HK VP70) Gaston came around.
I won't give it to Uzi either. He really knew how to make good things better but the telescoping bolt SMG design was developed by the Czechs first.
If I had to reach back and find another 19th century inventory, he wasn't even a gun designer. It would be Claude Minie who designed the minie ball. It made the basic infantry small arm as accurate as a rifle and loaded as rapidly as a musket. The conical bullet of Claude Minie lives with us today.