Indeed, the US pursued cultural export to Europe and Asia very aggressively, as a deliberate, planned policy [3] after the war. E.g. the Marshall plan granted convenient access to American film, pop music, and later on television to the Western European market [1] [2]. After the US built a huge culture industry, it was much easier to maintain momentum.
[1] https://journals.openedition.org/ejas/9701
[2] The World Audience for America's Story, US Advisory Commission on Information, 1949
[3] Coca-colonization and the Cold War, R. Wagnleitner, 1991