The assimilation goes both ways. American culture is heavily influenced by our immigrants. Looking at food, we Americanize practically any culture’s food, which may just mean changing the seasonings a bit (like making it less hot-spicy), swapping ingredients (Americanized Asian food in the US doesn’t commonly include organ meat), or branching out in tons of directions like we’ve done with pizza.
Irish, German, and Jewish immigrants have shaped a lot of our urban culture. Before Irish and German immigration exploded, the US was a whisky country, then it switched to beer. Germans introduced social institutions like kindergarten and fraternal societies that included the working classes (which eventually evolved into things like the American Legion) and of course workers’ unions. The three cultures greatly changed the religious makeup of the US from one dominated by British Protestantism to a pluralistic mix of Catholics, Protestants, and Jews. The US is the primary home of the world’s Jewish people (we have more Jewish people than Israel and the rest of the world combined, if you include mixed/secular Jews), and Jewish immigrants kickstarted the US’ involvement in industries like international banking and some kinds of manufacturing. Plus Jewish people have been hugely important in making US tertiary education and research some of the best in the world. Before these three groups immigrated, the US was agrarian and pretty homogenous, and these groups pushed the US towards cultural pluralism and assimilation.
In the modern day, Asian and Hispanic immigration are mixing things up too. I don’t have statistics but anecdotally I think Asian women are much more likely than other women to pursue careers in STEM, which has done a lot to make formerly male dominated jobs more gender inclusive. Spanish is basically a de facto co-official language in many areas. Americans outside these cultures are beginning to adopt multigenerational living (also because of cost of living) which is likely influenced by both of these. In almost all Asian countries, savings habits are very different than the default in the US, and I think you can see the effects of this in US areas with high numbers of Asian immigrants in things like property prices or a focus on value (like stores with lower margins and less marketing).
Basically none of these groups have been large enough to subsume American culture, but they’ve all contributed pieces on top of the base of Anglo Protestantism and culturally/actually genocided West Africans. And the sheer number of disparate immigrant groups have made the US the pluralistic society it is today, which is likely a big factor into why American culture easily exports to the rest of the world.