Cotton, hemp, and silk appeared by the 5th century BC, attesting to the extensive trade networks developed by the Greeks. Cotton originated on the Indian subcontinent, hemp in northern Europe, and silk in China. Several purple and white textiles found in a late 5th century BC tomb in Athens raise questions about when silk arrived in Greece.Hemp is straightforward. Herodotus talks of the Scythians to the north using hemp seeds in their baths.
Alexander the Great hit India a hundred years later, at the end of the 4th century, and clearly by then India was well known to the Persians. Cotton appearing in Greece in the 5th century via trade routes is very reasonable. Though there probably wasn't much of it. Most clothing was made of wool.
It's very unlikely--I'd go as far to say impossible to believe--that the silk road was open in the 5th century BC, but it's apparent that China was trading with Persia, Persia with Greece (when they weren't slaughtering each other), and therefore credible that some silk managed to make it to Greece.