Earlier Chinese Gunpowder

Around here Roman or Greek gunpowder threads are an irregular but popular subject. But what if the nation that invented black powder had managed to do so several centuries earlier? Specifically, I was thinking during the 3rd or 4th centuries after the collapse of the Han, the warring kingdoms, and the rise of the Jin dynasty. I chose this era because it's after Chinese connections to the outside world along the silk road had begun, and the exchange of goods and ideas was established.

Could gunpowder still be carried west by trade and nomadic empires like the Gokturks and Uyghurs like it did with the Mongols IOTL? Which powers of the early middle ages would be the best suited to take advantage of this new advancement, the Byzantines, Persians, Arabs, Franks? With Europe being considerably less developed than OTL would the tribes be steamrolled by their neighbors or could they adapt to the potential changes in warfare?
 
Was metallurgy developed enough then that gunpowder weapons could be feasibly used? I think I've heard that that could've been a limiting factor.
 
Was metallurgy developed enough then that gunpowder weapons could be feasibly used? I think I've heard that that could've been a limiting factor.
I’ve heard that too. If memory serves me well, I think that the issue was having the right kind of steel to handle the force of a gun. Something that didn’t exist in the west until around 900 or so, but had been around in China since the 300s BC or so. So either that metallurgy can make it’s way west sooner or be developed independently slightly ahead of time. For a third option bronze and brass can also work just as well for handling the impact of firing.
 
I've never been convinced by the metallurgy argument, certainly for Greece and Rome; surely a society that can cast bronze rams custom fit to ship timbers can make a bronze tube.
 
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