In the Tang period???
I know that during the Ming period they sent sea ships to East Africa.
But not earlier — as far as I know, they preferred merchants to come to THEM - so the Malay traders to India and Indian merchants onwards.
Chinese goods arrived both in India by sea and overland, and probably via at least one intermediary was involved to get the goods there.
There had been a Chinese expedition to Mesopotamia, which alas arrived not long after the abandonment of the Roman province there (Trajan added it before his death in 117, his boy-loving adopted son gave it up by 119). The delegation is known because they gave their report to the Chinese court, and the records survive. Perhaps because the Romans weren’t in Mesopotamia, the mission was considered a failure, but the distances may have been prohibitive. Probably the reason for the effort was the loss of Chinese control over the Silk Road and western interior. There had been a Chinese embassy to Rome itself (it sez here) in 97 AD.
The Romans picked up much of their eastern Asian trade goods in ports in India, but they also stuck in a toe at least once, as a vessel from the Roman Empire during the rule of Marcus Aurelius (121–180 AD) arrived and is recorded in Han Court records. By the time the Romans reached Han Court China, the dynasty was tottering, and not long after Marcus Aurelius died in the Roman Empire, uprisings started in Han China, and after decades of civil war, the former Eastern Han had been divided between three major states.
This slightly precedes the Romans’ Crisis of the Third Century.
BTW, the late Gavin Menzies basically fabricated his entire “Chinese discovery of America”.