Since the silk road is named after the fabric, it seemed a good idea to look at textiles that travelled along it and may have survived.
Until the Byzantine period silk was it seems exclusively manufactured into fabric in China and exported to the West. Then the Byzantines and Sassanians became the main source of patterned silk to the West (eg the silks used for relics of saints).
Although there are numerous references to silk - describes as fabric like glass - in Biblical and Roman sources, there are very few pre-Byzantine excavated fragments. The earliest silks were found at Sapalli-Tepe in Bactria (modern Uzbekistan), wrapped around four skeletons in tombs dating circa 1500 - 1200 BC. These are the oldest silks found outside the borders of China.
The first fragment in the West was a small piece of weave found in the 1842 at Kertch (here), and which came from China. The tomb has items similar to ones found in Late Ptolemaic Egypt and into the Julio-Claudian emperors, so the fabric is seen as a first or second century import. Although there was a sea route for trade with China via India, this silk probably came overland to Scythia from the Steppes - and stayed there rather than being traded on further west.
There were some questions about whether or not the Kertch fragments were made in China, since the pattern was unlike anything else known from the country.
Then before the war two small fragments were found at Palmyra, in tombs dated by inscriptions as built in AD 83 and in AD 103. Palmyran tombs were used by families for generations, so the silks are dated to the second century:
Those pieces were thought to possibly have been woven locally, because there is some evidence for silk production in Syria before the Byzantine period. Then a more elaborate fragment was found at Palmyra with a pattern that was clearly Chinese (now in the Musee Guimet, Paris). It may be second or third century, and pre-dates the destruction of the city in AD 272 (minor scraps have also been founf at Dura Europos, which was destroyed in AD 256-7):
What's interesting is that some tombs at Noin-Ula in Mongolia were excavated with Han silk textiles from China, and other textiles with Western patterns. Although the date of the Sampul Tapestry found in NW China is possibly second century but of uncertain date, these tombs are very well dated by an inscription of 2 BC on a piece of laquerware.