The US military was traditionally (until after 1945 - hence Eisenhower’s speech warning of the rising power of the military-industrial complex) rewarded (or punished, depending on your perspective) for winning wars by being dramatically down-sized directly after. For this reason alone, I think military capability has little to do with the capability of being a world power; the capability to rapidly put an entire country on a war footing and outperform your enemies in creating and supplying a military, as well as the capability to project power abroad, has a lot more to do with it.
Four examples:
In 1860, the US Army was largely state militias, only loosely grouped together into a whole with a unified command and control coming about only with the advent of war. Once the war started, however (and more so in the North than the South due to more industrialization) the Army was rapidly re-organized, re-armed, and re-trained with modern equipment. The turn-around was less than a year from a bunch of hick local state militias with obsolete weapons, training, and tactics to a unified, armed and modernized army that was the equal of any other country in the world. It took a bit longer in the South, but it still happened rather quickly.
In 1897, the military was tiny. It was called the US Army, but again was largely state militias joined together loosely at best and used largely for internal policing and western expansion with only occasional and brief extra-continental forays. Once the war with Spain started, however, again we had an incredibly rapid turn-around and the technology gap closed incredibly quickly and soon we were more well-armed and more modern then our enemies.
In the run-up to the Great War, the US was behind in nearly every military area - ships of the line, infantry arms, tanks, everything. Yet again, our industrial power led to an incredibly rapid re-arming and updating of our soldiers so that by the time they deployed our military was the equal of, if not the better of, any other European army and with a better logistical structure behind them to keep them full of ammo and beans and enough surplus production to help feed and arm our allies as well.
Finally, in 1938, the US military was a joke compared to any European power. Few soldiers, few guns, almost no tanks, airplanes, or ships; spare parts were sparse and hard to come by, and most of the weapons systems were hand-made rather than made through mass production - the M1911 .45 ACP pistol, the Thompson sub-machine gun, and the M1 Garand, staples of the US Infantry load-out in WW2, were hand-made until 1939 when they were started to be created through mass-production means. The Navy probably was the best off of any service and at least had a few modern ships especially battleships, but the Army was still flying paper-winged biplanes with hand-dropped small bombs in 1938. By 1940, the Air Corps was fully modernized and we were building dramatic numbers of ships, planes, guns, and tanks for lend-lease; further extension of this industrial capability after Pearl Harbor meant we were basically fully modernized as a military as well as outperforming any other nation on earth industrially to keep our troops in ammo and beans and again had enough surplus capability to feed and arm our allies as well as our own people with only limited conservation on our own people.
So to me, the key answer to the question of ‘when could the US have become a world power’ is as soon as our industrial capability and logistical infrastructure could support projection of power globally, could support the creation and maintenance of a large army capable of international operations, and could do both of those without too adversely impacting standard of living and capability of civilian industrial improvements.
So I would say somewhere around 1850 or so, although internal matters and politics meant it didn’t happen until much later.