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Looks like you've rediscovered Jaspers's concept of the Axial Age. However, if I understand correctly he did not posit that the Chinese and Western cultures influenced each other, but rather that they arose simultaneously under similar circumstances. Nevertheless, this might be a good starting point to explore from.
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There was no influence from China to the culture of Greece. Nor other way around. No Greek writer ever references a Chinese source, neither the opposite. Even more, the countries hardly could know anything substantial about each other.
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There probably were limited contacts between the Greeks and the Chinese, as the Hellenistic Greco-Bactrian Kingdom (250 - 125 BC) expanded in the Tarim Basin in northwest China. Strabo (64/63 BC – ca. 24 AD), quoting Apollodorus of Artemita (c. 130–87 BCE), mentions:
As for Bactria, a part of it lies alongside Aria towards the north, though most of it lies above Aria and to the east of it. And much of it produces everything except oil. The Greeks who caused Bactria to revolt grew so powerful on account of the fertility of the country that they became masters, not only of Ariana, but also of India, as Apollodorus of Artemita says: and more tribes were subdued by them than by Alexander—by Menander in particular (at least if he actually crossed the Hypanis towards the east and advanced as far as the Imaüs), for some were subdued by him personally and others by Demetrius, the son of Euthydemus the king of the Bactrians; and they took possession, not only of Patalena, but also, on the rest of the coast, of what is called the kingdom of Saraostus and Sigerdis. In short, Apollodorus says that Bactriana is the ornament of Ariana as a whole; and, more than that, they extended their empire even as far as the Seres and the Phryni.
"Seres" was the contemporary name for the inhabitants of eastern Central Asia and it means "of silk", or people of the "land where silk comes from." Alexandria Eschate was probably the first major Hellenistic outpost that came into contact with the Chinese, and the Dayuan that are mentioned in Zhang Qian's reports were probably descendants of Greek colonists.
These interactions were crucial in paving the way for the silk road. Though records of direct philosophical and religious exchanges between Greeks and Chinese don't exist, the two civilizations certainly came into contact, even if only indirectly via their respective contacts with civilizations of the Indian subcontinent. Buddhism spread towards the west was mainly because of the silk routes, and the various Indo-Greek kingdoms that followed the Greco-Bactrian Kingdom influenced it immensely, and Greco-Buddhist artistic elements can be traced in Chinese and even Japanese Buddhist art.