The short version is that we don't really know. We don't get references to gunpowder in medieval Europe until it was already fully present, i.e. it first appears in alchemists works in the late 13th century, we don't get references to 'mysterious exploding magic' from the east or anything of that sort. Most historians generally accept some form of narrative where gunpowder is invented in China (exact date of invention is somewhat contested), moved from there to the Middle East (we have accounts of gunpowder in the Middle East around the 13th century), and from there to Europe. The exact methods of transition, as well as the timeline, are sorely lacking in detail for us to fully fill them out. There's just a lot of gaps, and our accounts only are kind of dropping us en medias res, so we're stuck piecing together the early history of gunpowder from later materials and evidence.