> What if you dug a very deep hole, created a near-vaccuum, and you shot the rocket out like a rail-cannon?
What would happen is your payload would follow a ballistic trajectory up through the atmosphere into space, then it'd fall back down and hit the ground somewhere west of the hole because earth rotated under it while it was in flight.
As XKCD puts it, "The reason it's hard to get to orbit isn't that space is high up. It's hard to get to orbit because you have to go so fast." https://what-if.xkcd.com/58/
Also the way 2-body orbits work, you will always return to the point you last changed your velocity. That means your hole-launched spacecraft's flight path is actually an elliptical orbit that's so extremely narrow that it looks more like a straight line up and down, and then the ground prevents the vehicle from continuing on its orbit around the Earth's center of mass. So if you want to "circularize your orbit" you have to increase your sideways velocity by thrusting at the top of your orbit, so you can as Hitchhiker's Guide puts it "throw yourself at the ground and miss." That way the ellipse is mostly a circle around the Earth and you'll return to that thrust point in space rather than returning to hole's entrance.
So you'd want to make the hole more like a train track running just under the surface (or an evacuated tube just above the surface). That's sort of what SpinLaunch and other non-rocket space launch systems like mass drivers and Project Babylon.