But this just isn’t true! The U.S. overtook the UK in per capita GDP in 1880, near the peak of the British Empire: https://unchartedterritories.tomaspueyo.com/p/us-gdp-per-cap.... At that point the UK was already significantly richer than the rest of europe.
If you look at GDP growth rate, the US has consistently averaged 1.7% GDP per capita growth over the past 200 years. The mass industrialization during the war itself spike growth and helped recovery from the Great Depression, but America didn’t grow dramatically faster during the NATO era than it did before that.
The U.S. is rich because its been one of the richest countries in the world since the 18th century and has been extraordinarily stable. It was considerably richer than western Europe even going into the 20th century: https://www.researchgate.net/figure/Population-GDP-and-GDP-p.... In 1900, U.S. gdp per capita was almost 50% higher than western europe. In 1990, it was also about 50%. There was a temporary period right after the war when the U.S. was much richer than western europe, but europe actually grew faster during this 1950-1990 period.