That was somewhat after the founding of Rome. There would be no reason to suppose that Rome was not in contact with China all along.
Han Dynasty came close to contacting Rome. They had a 100,000 man military expedition that got to the Caspian Sea and decided to head north. If they had headed south, they would have entered the eastern outposts of the Roman Empire. The Persians were buying silk from China and selling it to the Romans. The same happened to Alexandra the Great. When he headed an expedition going east from a region known today as Afghanistan. He hit a major mountain range that bordered today's Sanjing region of China. Alexander thought that was the end of the world so he stopped and went back to where he started and turned south into India. If he had gone over the range he would run into the western outpost trading cities of the Chinese civilization (China was not united yet, but had six major kingdoms)