It should be understood that until the 1500s artillery was exclusively siege. Actually, the first case of the use of light field artillery was in 1467. The carriage of a heavy siege gun was then a wooden box in which this gun lay. At the firing position, this box was placed on a special earthen embankment. And they were transported by loading them into wagons, as well as other military equipment. Accordingly, the artillery moved along with the baggage train and with its speed. Moreover, due to the large weight of some guns, bulls were often used instead of horses in carts (up to 16 pieces per cart), which further reduced the speed.
From about the middle of the 15th century, carriages began to be mounted on light wheels (with spokes) ) of large diamet, which gave rise to the stable use of field artillery. In the middle of the 16th century, charging boxes (front wheels) were invented, which further increased the mobility of artillery. Field artillery was then part of ordinary military detachments and moved with them.
At the end of the 18th century, the horse artillery was organized. The staff of the guns moved on horseback. The horse artillery was able to accompany the cavalry on the move.
Of course, all this is said only about the most general practice. Rare cases are out of this chronology. Moreover, in these exceptions, the use of artillery was very limited.