Nuclear weapons were developed by the Soviets before the end of the 40's, so it was a very narrow window where the US was the sole holder of all nuclear arms (about five years).
Five years is an eternity though. The major factor was more likely we didn't have the capacity to produce a large number of nuclear weapons to tip the balance
Huge power imbalance between USA (sole holder of all nuclear arms), and the rest of the world.
So ... yeah, kinda proves your point.