In the immediate post war era, the US was the first large economy of its kind to get the kind of things we take for granted now. I'm talking TVs, basic appliances, etc. Home ownership and automobile ownership. Why exactly the US was the first to get that explosive growth in all these areas is not something I am qualified to answer, but it's important to note that perceptions of America's 1950s "Golden Age" is in part due to the simple fact that America then had a huge advantage over other nations just because it was getting things first. We no longer idealize TVs, refrigerators, mass car ownership, etc. as huge economic achievements because many other places have them. European countries experienced explosive economic growth too, but it took a little longer with them.
Also to add to the other responses above, it should be remembered that economic rebounds after a long economic slump are often that much more powerful depending on the economic slump they are following. When recovery does come, the perception of recovery fuels more spending, more investment, more optimism and hence a stronger recovery. And of course, economic slumps breed immense opportunities for growth. The People's Republic of China provides an extreme example of this; after several decades of Maoism and really fairly terrible economic growth, the PRC economy went through the roof in the 1980s, and that was due, in part, to the simple fact that the PRC was starting from somewhere close to zero economically speaking, when compared to the rest of the world, so it had nowhere to go but up. Though much less extreme, the pattern was also evident in America in the post war era.
Overall, it can be argued that America's post war "flourishing" was really a relative perception that we have looking back on it, based on how we were doing compared to other nations now.