What belief system would have been MOST likely to have traveled from the east to the west during this time?

The religious beliefs of people along the Silk Road at the beginning of the 1st century BCE were very different from what they would later become. When China defeated the nomadic Xiongnu confederation and pushed Chinese military control northwest as far as the Tarim Basin (in the 2nd century BCE), Buddhism was known in Central Asia but was not yet widespread in China nor had it reached elsewhere in East Asia. Christianity was still more than a century in the future. Daoism, in the strict sense of that term, connoting an organized religion with an ordained clergy and an established body of doctrine, would not appear in China for another three centuries. Islam would be more than seven centuries in the future.

A. Buddhism