Handguns - ones that could be aimed, and so were effective- came in with the discovery of how to better manufacture consistent gunpowder in the 14th c., and were gradually more and more common on the battlefield in the 15th. You would find rather heavy ones used for the defense of city walls in Germany ( as they commonly had hooks at the muzzle, they were dubbed Hackbuchsen, which became the name arquebus) and they were part of the weaponry, along with crossbows and halberds, deployed behind the walls of the mobile fortresses, or Wagenburgen, of the Hussites , circa 1419.

The loading and firing of a matchlock gun was complex: managing a smoldering length of lit match while also handling gunpowder for loading and priming took some time, skill and care, especially in the midst of armies and cavalry maneuvering on a battlefield. So, it's not surprising that there would be a variety of arms used in the 16th c.: crossbowmen, soldiers with matchlock guns, soldiers with pikes and polearms, armored cavalry with lances, heavy artillery. Though there's no real definite moment in which guns became common and bows obsolete,, a useful date is 1525, in the Italian Wars: during the Battle of Pavia the Spanish were able to use their troops with arquebuses to defeat the French heavy cavalry and Swiss pikemen/halberdiers. After that date, pretty much every European conflict would have infantry with both guns and pikes. That mix of "pike and shot" would continue into the 17th c., until around 1700 bayonets were introduced that didn't plug the muzzle of the gun. That invention made pikemen mostly obsolete, as troops with muskets could quickly and effectively be transformed into pikemen.