In fact, they did:
Chinese-Roman relations: The contact remained linked through the Silk Route, when both Romans and chinese expanded through Asia it was inevitable that they would find or at least heard of each other, still, the first recorded meeting was around 166 AD when the Romans sent an emissary to China. There have been found Roman coins minted from the 1st century AD onwards.
Chinese-Greek relations: The contact between these two factions was basically done when Alexander the Great expanded through Asia in his Hellenistic campaign. There is evidence of Mediterranean gifts found in the tomb of the greatest emperor of China, Qin Shi Huang. It is said that there were Chinese emissaries in Alexander's court but their name wasn't "Chinese".
Chinese-Babylonian relations: There is a theory that the Yellow Emperor that unified China was in fact a Babylonian who migrated with his people to what is now China. Still, it is still being considered.
Chinese-Persian relations: Since 200 BC there were relations between these two cultures. They were linked economically and culturally through the Silk Road and the Persians were known as the Parthians and Sassanids. Both of the Chinese and Persians were even under the rule of the Mongol Empire for a while.
Japanese-Persian relations: They had some contact around 700 AD, and that follows with the Romans if you could say so since Japan was a little state under the rule of China at the change of era (0 A.D.)