China's recorded history goes back more than 3000 years. Granted, it was only unified 2200 years ago.
I don't know if any possible interpretation of Chinese history that puts China's formation a mere 500 or 1000 years ago. The Qin dynasty (3rd Century BC) is really the absolute latest point at which you could say China came into existence.
It's more like the British harkening back to Chaucer's England.
The problem with the Rome analogy is that China has had much greater continuity than Europe. China is what Europe would have been, if the Roman Empire had been reconstituted each time it collapsed.
Imagine if there were still one political entity ruling the entire Mediterranean basin and Western Europe, calling itself "Rome," speaking a Romance language, and in which every educated person was still capable of reading the Latin classics (with some difficulty).
I don't know if any possible interpretation of Chinese history that puts China's formation a mere 500 or 1000 years ago. The Qin dynasty (3rd Century BC) is really the absolute latest point at which you could say China came into existence.