It turns out that the Classical world had silk, which was not even from China!
Instead, there was an Agaean island called Kos (or Cos) that produced silk from the local silk moth, Pachypasa otus, which ate local trees and produced white silk cocoons that were processed, spun and woven. The Roman patricians used it, too, especially dyed red or purple. Caligula was said to dress in silk, and Elagabulus supposedly required a brand new silk garment every day.
This is so exciting!