Colt's 1836 revolvers were cap and ball, and cartridge revolvers didn't gain wide acceptance until 1873 when Colt introduced the 'Peacemaker.' After that, it took a while before another genius, Hiram Maxim, in the 1880s, realized that recoil energy could be used to eject the spent round and simultaneously compress a 'recoil' spring to pick up and chamber another round from a belt, and a belt is a flexible magazine of sorts.
The first practical machine gun was Dr. Gatling's gem and he possibly stole the idea from a Leonardo da Vinci design of centuries before. The Gatling was a large, heavy beast on wheels and thus did not get wide acceptance although its principals remain in use today. Following the Gatling, it was another 20 plus years before Maxim figured out how to use the wasted energy of recoil to chamber another cartridge automatically and the machine gun, pretty much as we know it today, was born. Following that, Borchard, Luger, Browning, and many others came up with mechanically simple, compared to a revolver, self loading handguns. Browning didn't invent auto pistols but his genius was in figuring out how to introduce a mechanical delay (the drop down barrel, etc.) which permitted much more powerful rounds to be fired from relatively light pistols and the 1911 45 was born. Actually Browning completed his design about 1906 but it wasn't accepted by the Army until 1911, hence the 1911 designation.
If you know handguns, you'll know a DA, even a SA, revolver is a complex firearm and requires precision to manufacture, assemble, and fit the parts. The cylinder has to be precisely machined and fitted so each chamber lines up with the barrel, and it has complex combinations of cams, gears, pawls, and springs to rotate the cylinder, lock it in place for firing, cock the hammer, and so on. Even the mechanisms to swing out the cylinder and eject the spent rounds are complex. I know because I've repaired and tuned hundreds over the years to make them function correctly. Give me a simple auto anyday to repair vice a revolver...!
Autos require none of that complexity to function. Most auto pistols today combine the slide and bolt in one piece. When a cartridge is fired, recoil drives the slide back, extracts the fired round, and ejects it. The slide/bolt recoil spring is compressed and when it returns the slide/bolt to 'battery,' it picks up another round from a mag and chambers it. At the same time, the recoiling slide/bolt cocks an internal striker or external hammer. All of that is mechanically simple compared to a DA revolver!
As for Colt not having sophisticated technology available in 1836---Bull! By that time the world had railroads, steamships, printing presses, and factories mass producing countless products---clocks, surgical and navigational instruments, farm implements, tools, utensils, toys, furniture, clothing, implements of war, and on and on. Do a little research and learn how advanced the world had become by 1836. Hell, the Brits were madder than hell at us long before then because we 'Yankees' were mass producing accurate and cheap clocks which drove many Brit and European clock makers out of business.
Read 'Development of the Gun' by Greener if you want some insight into just how advanced machining, mettalurgy, and so on had become by the 1830s. They even had accurate mechanical chronographs 150 years back and methods to accurately measure breech and barrel pressures. They produced black powder and percussion caps in vast quantities and with very tight quality control. When that Scotch pastor invented percussion caps about 1807 or so, he started a revolution in guns. Although the Brits did keep the Brown Bess flintlocks in service for another 30 years probably due to the expense of changing over to percussion caps.
Well prior to 1836, the US also mass produced firearms although all were single shot and muzzle loaders. However, remember that during the Revolutionary War, a Brit officer and his unit were equipped with breech loaders and it was sheer luck Washington wasn't sniped with one or so the Brit officer later claimed. Anyway, experimentation with breech loaders, self loaders, revolvers, etc., was going on all the time.
IMO, Sam Colt assimiliated available technology and didn't invent anything radically new to come up with his first revolvers. There were many other similar designs and prototypes in progress at the same time. Colt's just happened to be the first that worked reasonably well and could easily be mass produced. BTW, Colt used Brit and European funding for his first guns. Hiram Maxim had to go the same route and sell his first machine guns in Europe because they weren't, at first, looked on favorably here in the US.