Nationalism relies on the premise of constructing who belongs to the "nation" and how they belong based on artificial social characteristics. You can't have a nation without in-groups and out-groups, natives and migrants, borders and a military to defend them; properties of the state. You could say there are various groups of "peoples," constituents of the human species, that differ between each other in various ways (though I'd say in a broad continuum), but without the state to literally enforce what it means to be part of the "nation," it does not really exist. Not in a positive way at least, dividing people up into different arbitrarily defined "nations" is good if you like war and conflict thought I guess.
Let's just take language for an example: with the creation of modern nation-states with state directed mass educational systems, languages had to be standardized; orthographies had to be codified; dictionaries had to be written... so that children could be educated into speaking in one way. Before the modern nation-state, languages were constantly in flux, you might have trouble understanding the dialect of someone from the next village over (even though it's the same "language"), let alone in a different "country."
This whole process is why even today many languages are dying out and giving way to the biggest/most spoken languages (sponsored by states).
It doesn't stop at languages either, the state does this with all facets of "culture" and "tradition."
Languages aren't artificial. Languages are very much real.
Standardization of languages and merging of dialects\languages in one require... languages to exist in the first place. If you define nation=people speaking language X (BTW it is exactly what modern Russian ideology says) then you must admit that nations existed since... forever.
Do I claim that before, let's say, united Germany there were many German nations? Yes and no. The universe doesn't fit human obsession with creation of well-defined categories of anything. There are no defined boundaries between nations, it is always a gradient and you can always zoom in or zoom out. Germany had (and, to lesser extent, has) "subnations" and together with Austria they form a "supernation", and they are also a part of a European "supersupernation". It is complicated
At its core, nationalism is "we are similar people we want to live in one country and govern ourselves", you claim that it is "We live in one country and govern ourselves and it makes us similar people" but if it worked this way, there would be no separatist movements whatsoever.
As for the USA... Do I think that the USA qualifies as one nation? Yes. And no. Depending on how far you wish to zoom in, on how you define a nation.
Do Dogs and Cats belong to the same group? We can say yes, both are Carnivora. We can say no, Canines and Felines are clearly different.
Unlike biology, where there is no DNA exchange between cats and dogs, groups of similar humans (nations) exchange DNA (bits of culture) with other groups of similar humans, creating a spectacular mess.