We've been there, done that, spent millions, abandoned it. HARP
Even Saddam Hussein got in on the action.
See Project Babylon
Didn't quite get a bullet into low earth orbit, however. An assassination and a Gulf War stoped it.
However, what you need is answered by
As a result, all payloads intended to reach a closed orbit need at
least to perform some sort of course correction to create another
orbit that does not intersect the planet's surface. A rocket can be
used for additional boost as planned in both Project HARP and the
So the long and the short of it is, no you can not get a projectile into stable low earth orbit using just a gun.
The gun still exists, if you want to give it a shot.