Yes, a "nation" may be defined as group with common origin, but the word is used synonymously with "state" nowadays. So while the US may not be a "state" with the same "national" origins as others, it's still on equal footing with states who derive their identify from ancestral origin.
At any rate, a better country to explore might be Singapore. Having spent some time there, that is truly a "state" looking for "nationhood". It was a British colony for a while, populated by a mix of Chinese, Malay, Indians and Westerners. It briefly joined Malaysia, but then was kicked out.
It's amazing the effort the government puts in to nurture a sense of national identity, it most certainly didn't come naturally - one could argue Singapore had the most stacked against it - a mix of ethnicities, many who strongly identified with their homeland, a history of a trading port with a transient population, and no heroic story of independence, rather an independence forced on it.
Government programs like HDB (home ownership), national service and racial policies to prevent balkanization have gone pretty far in creating a Singaporean identity. But I get the sense the govt feels it could go the other way just as easily if allowed to wilt.