It's extremely unlikely that many people outside of Jesus's broad social circle, and perhaps a few of his antagonists such as pharisees or Roman authorities, would have known about Jesus during his life time. At least as far as written records (that we still have!) go, I don't think we have an earlier date for Christianity than when Nero turned some of them into lion chow in 64 AD, about 30 years after Jesus's death.

I wouldn't say it's impossible that some Levantine trader might have told a story about some weird self-proclaimed prophet in some Chang'an tea shop, but it's not likely, and not supported by a shred of evidence.