Keolah makes a good point about weapons in general as technology. Firearms existed alongside knights and melee-armed infantry for a long time. What really pushed the rapid development of firearms in Europe was the advent of the Swiss pike and shot regiment, which overcame the battlefield monopoly of feudal knights with a combination of high-quality pikes, massed arquebus fire, and most importantly -training- to NOT BREAK when several tons of horseflesh and armored men (who have lived their entire lives as martially dominant nobles) bear down on you. Once heavy cavalry lost its dominant place, the ease of training and manufacture of firearms had a snowball effect, in which kingdoms (and eventually nations) conscripted and trained ever larger quantities of infantry, thus necessitating and reinforcing the development of better and better guns. It really wasn't until the 19th century that rifles obsoleted horses on the battlefield, at least in large-scale warfare.
But I think a new angle to consider would be the development of gunpowder weaponry in places other than Europe. Guns and cannon were only two potent weapons in the Chinese and Mongolian arsenals. One of the many reasons firearms did not develop as swiftly in the Ming Dynasty (1368-1644) was because the main enemy of the Ming - the Mongols - still used quick, light-cavalry tactics and did not deploy massed infantry. Early firearms were much less effective against these peoples: guns were less accurate than crossbows (or bows wielded by trained men) and so soldiers had a harder time hitting fast-moving horse archers. Small cannon, however, were quite ubiquitous among imperial armies, especially on the Great Wall. The problem came when Ming emperors (especially the early ones) tried to march into the Mongolian steppe and desert, and the extreme logistical considerations of those campaigns made the movement of cannon really difficult. So larger cannon were used almost exclusively for 1) walled city defense and 2) laying siege to other walled cities in times of rebellion, when Chinese fought Chinese. When Mongol rule crumbled in China in the 14th century (before the founding of the Ming) and multiple Chinese kingdoms rose (mostly in central and south China) to fight for imperial power, cannon and firearms were used quite extensively, since their armies inevitably used large armies of conscripted infantry.
So assuming firearm dominance as the natural developmental course of weaponry is quite a Eurocentric point of view. It's not -wrong-, really, but there are other ways of thinking about it. I think the OP's situation, where mages are quite rare, would absolutely leave room for the rapid development of firearms, as people sought better weapons to fight other kingdoms' armies. You may want to consider, however, that if ground forces would want to "snipe" wizards, they would use cannon or crossbows.
Overall I think it's awesome to see more gunpowder weapons in fantasy! Medieval Europe has been done to death. Let's try non-medieval but still-European fantasy!
EDIT: My own story takes place in a fictionalized, fantasized China, and both cannon and infantry firearms are quite common. When the empire in my story makes war against the northern nomads, they use cannon but not firearms. Against the southern peoples (who tend to use infantry, and also sorcery), firearms come into play. So different armies in my empire use different weapons.
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