Real history or propaganda? Impossible to know these days. Liars and revisionists have made everything suspect, especially if it can be spun to a political narrative.
They came 20,000+ years ago.
That was at least 16,000 yeare before there was the first real “Chinese” state of the Xia dynasty. The Han people called themselves the Huaxia people around 2200 BC.
20k years ago, there was no China, no USA, no Chinese nor English nor even proto indo European language nor Tibet burmese language.