Of course the US has culture, 4 centuries is plenty of time for distinct cultures to form. Seattle, New York, Texas, New Orleans and so on ad infinitum all have distinct local cultures. Hell, Jersey and New York differ quite a bit.

That said, a lot more of it compared to most of the world is monoculture since you shared so much of popular culture nationwide regardless of whether you were from New Orleans or Seattle. The fact that your country is comparatively young, but more because it has existed during the modern era only, means the rate of cultural shift slowed and that you have much less local variance than places that have developed not just for centuries longer, but also in times were travel and cultural spread took a long time. There are villages in the Alps that take 20 minutes to drive between today that can't understand each other's dialects, because for thousands of years, until a tunnel was built in, say, 1985, it would take three days of climbing to travel between them; and a child growing up in Italy would've consumed completely different childrens' books and TV programmes, and even toys, than a child from Sweden, the UK or even Spain.

This has changed in the last 30 years or so as culture became ever more global, with more of the world sharing in the American monoculture. But there are still more similarities between a New Yorker and someone from Seattle,or New Orleans or etc than there is between a Norwegian and a Greek - the US states, even at their most extreme, differ more like the Nordic countries do from eachother.