There are a couple of reasons that American culture proved to be a beacon for so many in the 1950s. Emerging as the victorious power from the West out of World War II, the consumerism, perception of independence, as well as the prosperity that were intrinsic to American culture in the 1950s was something that so many other nations sought. American culture represented success and individual drive, an embodiment of the idea that a person can find prosperity through hard work and dedication. American culture embodied this to so many in the world, who, themselves, were learning to either dream for the first time or dream again.
Europe had been decimated by the Second World War. Axis or Allied powers, all European nations struggled to rebuild in the wake of the Second World War. American culture demonstrated itself to be the model that these nations examined in the hopes of rebuilding their own nations. The investment of the Marshall Plan helped to construct the vision of American culture as holding promise and possibility within it. The destruction of Japan through atomic warfare set the stage for its rebuilding, in which a democratic, market- based economy similar to American culture was understood as the only acceptable path after years of Emperor rule had led Japan down such a destructive road. At the same time, Eastern European nations that had been taken over by the expansionist Soviet Union believed that freedom and opportunity, in short a better life, would be more evident in American culture. Though citizens in these nations did not dare to say it, there was a mystique about American culture that proved alluring. This helps to explain the rise in immigration to the United States during the 1950s.
Other nations around the world found themselves emerging to nationhood status in the wake of the Second World War. For nations seeking to establish their own identity, American culture became defining. It represented material success that people in new nations wished to have for themselves. American culture represented where citizens of these nations wished to be. In the end, the people of these new nations were less persuaded by the Communist notion of the good, as seen in the Soviet Union. They were more persuaded with the potential opportunity to be like "Americans." They believed that if they could model their own social orders to be like American culture in the 1950s, there would be a greater chance of them finding happiness.
There are many ways in which to answer this question, but let me answer this question by looking at what the world was like in the 1950s.
In the 1950, Europe was in the process of rebuilding, as the largest war in history was fought there. Hence, they were too busy rebuilding their lives, infrastructure, and economy. These were times of difficulty. For America, it was a time of prosperity. The war to end all war was finished and won. Moreover, America was in tact. They could launch off into a period of growth.
When we move over to Asia, it was still developing. The strongest Asian nation of the time, Japan, had been defeated in war. In fact, it was still reeling from two atomic bombs.
In short, as great as America was in the 1950, it was the only show in town. All eyes were on America. The potential of continued growth was there.