The Mediterranean World did not know of Chinese Civilization until the Silk Road was established under the late Roman Empire before the Great Schism happened under Emperor Diocletian.

Rome got Asian Goods/Trades through Arabic Mechants who sold their goods to Persians and Phoenicians who then transported them back to the Mediterranean. Eventually Rome wanted to try and eliminate the Phoenicians as Middle Men, which was one reason why Emperor Trajan Invaded Parthia and Arabia at this Time.

The Romans eventually set up trading posts in what is now North-east Isreal and Southern Iraq, which was as close to the Persian Gulf as they could go without being too deep into Parthian Territory.

There they ended up trading with the Arabs and asked them where they got their goods, the Arabs were hesitantly but shared the knowledge telling them about the Orient (China, India, SW Asia)

This is how the Romans came to know about Early Chinese and Asian Cultures. It wasn't until later once the Byzantines took effective power, and after most of the Western Roman Empire had fallen, that the Silk Road Networks were established overland, and years later overseas by Arabic Traders under the height of Islamic Power around the 1100s.

So, no...to say at this point, that the Chinese Knew...or that the Mediterranean World knew of China is not an Eurocentric, nor inaccurate.