The US had almost no nuclear weapons prior to the Soviet Union getting nuclear weapons (lots more details on this here), but, frankly, the main problem here is that you have overestimated the importance of nuclear weapons in "taking over the world." To hold any political territory still requires "boots on the ground," and the ability to even launch nuclear attacks in the 1940s was predicated on having territory reasonably near the target (there was not yet any global nuclear capability). A US effort to "take over the world" (which is just a silly notion anyway — taking over the entire world is not viable, not even desirable, compared to a lot of other outcomes, like making sure that there are favorable regimes in different parts of the world and that they will trade with you) would alienate those allies, stretch the already war-weary US military thinly, infuriate a significant portion of the US populace, and probably result in things like Soviet conventional forces taking over Western Europe (perhaps at the loss of a few Soviet cities, but the US did not have an arsenal large enough to do a "all in one" sort of doomsday strike against the USSR).

The idea that the possession of nuclear weapons gives a country unlimited latitude is entirely false, even if that country is the only one with them. The world is much more complex than that, with intertwined political alliances, economic requirements, and so forth. The atomic bomb is a potent weapon, but it is not an unlimited weapon, especially in its 1940s incarnations, where it was of relatively limited strength (atomic bombs of the 1940s varieties could more or less take out the downtown of a major city, or destroy a medium-sized city), limited number, limited reliability (the first generation of nukes had a relatively high chance of failure and were difficult to assemble and use), and limited deliverability (B-29s).

The US had atomic primacy for an extremely short period of time. The US tested its first atomic bomb at Trinity on July 16 1945. The Soviet Union tested its first atomic bomb at the First Lightning test on August 29 1949. That's four years and one month to take over the world.

Moreover, even though the Soviet Union didn't have the bomb, they still the largest and the most powerful army at the end of World War 2. Early Cold War Army doctrine called for nuclear first strikes as a defensive measure against Soviet invasion, as it was taken for granted that NATO conventional forces wouldn't be able to hold out for long against a Soviet combined-arms assault.