Han Chinese defeat Roman legionaires 36 BC?

[Theodosius the Great]

Oh I don't doubt that there was a lot of incidental contact. I have no doubt that Romans could have been in the Chinese court at a very early date, but those numbers would have been few, and their impact very limited

Here's something interesting from Wikipedia :

Contacts with China
The first of several Roman embassies to China, although attributed to Antoninus Pius by the Hou Hanshu (History of the Later Han Chinese dynasty), was probably sent out by Marcus Aurelius. Antoninus Pius died in 161, while the convoy arrived in 166. The confusion arises because Marcus Aurelius took as additional names those of his predecessor, as a mark of respect. The emperor is referred to in Chinese history as "An Tun" (= Antoninus). The mission reached the Chinese capital Luoyang in 166 and was greeted by Emperor Huan of the Han Dynasty. However, in the absence of any record of this on the Roman side of the silk road, it may be that the "ambassadors" were in reality free traders acting independently of Aurelius.