Also, in terms of more tangibly visible aspects of American culture that you don't normally think about but are definitely American:
Music: Jazz, Hip-Hop, Rap, Country, and Blues are all inherently American music styles that have spread worldwide
Religion: many of the various major Protestant Christian denominations that exist were founded in the United States. Baptists, Methodists, Episcopalians, Quakers, the AME and other African American churches....you just do not get the same Vibe⢠anywhere else. The history of Christian evangelism/evangelical churches is embedded in our culture. The American South is called "The Bible Belt" for a reason, and that reason is the existence of a particular unique culture that gets exported elsewhere.
Also...Jehovah's Witnesses and Mormons. Both are "fringe" but largely inescapable parts of American culture.
Architecture: Art Deco, skyscrapers, the concept of American suburbia
Technology: the pervasiveness of Apple/Apple products as a cultural signifier of wealth and status
Clothing: wearing a baseball cap abroad is literally the easiest way to get identified as an American. Also, our 'casual clothes' culture compared to most other countries
Holidays and Traditions: Thanksgiving and Memorial Day are the two most notable holidays with unique cultural characteristics and traditions
Sports: American football and baseball, but also "regional" sports like ice hockey, rodeos, and lacrosse....also, frankly, the way that sports and sports teams are integrated into the school system. That's largely unique to United States culture. The concept of Homecoming straight-up doesn't exist in most other countries. Related: the Kentucky Derby and horse racing as social events, golfing as a part of American business culture
Literature and Media: Disney, caped/masked superheroes, the Transcendentalist movement, Slavery narratives, the Beat Generation, late-night talk shows
Other general pieces of American culture: driving at 16, high school prom, car and driving culture, volunteerism, gun and hunting culture, and our weird cultural relationship with alcohol and drugs due to the history of the Prohibition movement and the War on Drugs
It's important to realize that it's often difficult to see a culture when you grow up in it and doubly difficult when your country is a culture exporter (sometimes in the name of cultural imperialism, sometimes in the name of making money, and sometimes by complete coincidence). But the United States definitely has a (or a series of) culture(s), and it is in many ways a sign of American exceptionalism to pretend we don't.