The Silk Road wasn't one continuous chain bringing goods from China to Europe. In reality it was many different largely self contained long distance trading routes that only at a considerable remove begin to look like a single one. For example, a very important trade route was the so-called "tea horse road" would involve the transport of goods between Sichuan and Tibet. In turn, there were significant routes between Tibetan and Bengal. From Bengal goods might be carried around the coast of India, say to Gujarat. From Gujarat in turn there were routes going up the Red Sea and the Nile to Alexandria. And from Alexandria they might arrive in Italy. At no point was anybody thinking "I am carrying these Chinese goods to Europe"--traders would only be concerned with their immediate origins and destinations. So if a good managed to make it all the way from China to Italy, it was only because it had commercial value at every stop of the way, and yet wasn't sold off entirely at any individual stop. What changed in the sixteenth century from a Europe perspective is that European sailors themselves started to get much closer to China.

In fact, it is worth noting that the Silk Road as a concept is pretty Eurocentric, often being seen purely from a European perspective. Aside from marginalizing the many societies in between, it is explicitly focused on the goods that arrived in Europe despite Europe not being a particularly important part of it.