Is someone born in the US a citizen of the US at birth?

As long as you were born in the USA, and there is documented evidence of your being born there, you are an American citizen. An extreme example would be an American Prisoner of War, held for years, or decades, against their will in Another Country. They are still American citizens no matter how long they remain outside of the USA geographical borders. Unless you voluntary give up your citizenship, you are still an American, no matter where you live.