Everything comes from somewhere else. Beans, corn, peppers, potatoes, squash, and tomatoes all came from the Americas. So any culinary traditions using those ingredients only goes back at maximum early 1700s, but more like early 1800s. They pale in comparison to the many centuries of history they have on this side of the ocean. Native people have been nixtamalizing corn for longer than anyone has been speaking French.
The UK has distinct food culture, that's not at issue. But you can trace it to the density of people and length of time inhabited. But if you look at specific regions of the US, you can see similar. Take a similar size area. Like the northeastern seaboard from Boston to north Carolina, that's a HUGE amount of regional food differences. Beans, soups, seafood, sandwiches, barbecue, fried chicken, breakfasts, desserts, slaws and salads. And that's not even mentioning the alcohol traditions. Scotch wouldn't exist without used American white oak bourbon barrels.
But yes, I am making the argument that both Mexican and Chinese food in the USA are separate and culinarily distinct things than what you find in their home countries. They've been in this country for well over 100 years; living, evolving, changing the attitudes and palates of Americans the whole time. You won't find most US Chinese dishes anywhere in China, and you won't find a dish that looks like US Mexican or TexMex in Mexico, even if it's got the same name. But they will be regionally different. They're influenced by each other, but they're separate.
More than that, I'll give you three foods that evolved from elsewhere but finalized in the US, and three honest foods that are 100% from the USA, showing off deep food culture. First for the evolved dishes that now are around the world. Hot dogs, hamburgers, and fries. They all had precursors, but the combination of German/Belgian food, French baking, and food science with industrialization to make for a cheap food that is tasty and easy to eat? Purely American. And now exported worldwide.
Next are the cultural dishes. First is chili. Every state has some version, some variety. With or without beans, different protein, brown or white, and different spices. But it's a dish that comes from hard work, long hours, and wanting a filling meal that's easy to make but well spiced. No bean soup quite hits the same highs, it's almost more of a stew. Then you have biscuits and gravy. It originally came from the Revolutionary War, but today it's best recognized as southern love on a plate, and and just as many calories. People from the UK often confuse US biscuits for scones, but they're not. Scones have egg, and usually sugar in the dough, and get worked 2-3x as much as a biscuit, which is crispy on the outside but inside is airy, light, fluffy, and savory. Goes well with the rich, creamy, peppery sausage gravy. Last is barbecue. That's got 5 legitimate culinary traditional regions and probably like 4 more that could argue for another. But it comes from poverty and slavery, when people couldn't get good cuts of meat and had to invent methods to make them good. Then they combined that with Afrocaribbean flavors and local ingredients, and you have a unique tradition that is probably some of the best open heat cooked meat in the world.
After all this, I'm really not some sort of American chauvinist. Honestly I prefer pasta, ramen, and some African foods most of the time. But everywhere I see this lie that the USA has no food culture and it drives me wild. It's a rich and diverse food culture, but just very different than the media says and very different than the rest of the world, and especially Europe. So it can sometimes be hard to understand. Hopefully this helps.
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