A guidance system
The age of cannons is over. The age of RPG's, ICBM's and Air-to-air missiles is not. What caused this?
A cannon projectile is a stable system. Once launched from the muzzle of a gun, it's flight path is relatively predictable - it follows a parabolic arc. Sure, it's not 100% accurate due to tolerances between the bore and projectile, but it's not too bad.
A rocket is a much less stable system. If a rocket gets any angular velocity on launch could end up literally anywhere. It needs something to keep it straight. The simple solution are tail-fins. Tail fins are good, but if they are off by a degree or two you end up with rockets that fly in circles.
Rockets only really became useful after guidance systems were invented. Initially these just kept rockets on a straight line, but eventually they became active guidance systems using lasers, GPS, inertial measurement systems etc.
Once this point was hit, rockets became steerable explosive shells with longer range than cannons.
Ever notice there aren't any large bore guns on modern battleships? That's because a bunch of missiles is superior in every way except for cost. As a result battleships were largely replaced by guided missile destroyers.
What resulted in the development of guidance systems?
I suspect that rocket guidance systems largely evolved from torpedo guidance systems. Torpedos are slower and easier to control, and the first solution for guidance seems to have been in 1866 using ... clockwork and compressed air.
Could this have been developed sooner? Maybe.
What's next though?
Are cannon gone forever? Maybe not. Railguns allow much lighter-weight and cheaper ammunition, and can shoot at incredibly long ranges. I strongly suspect that guided railgun projectiles will be a major future long-range large-damage weapon.