Rockets launched to reach orbit usually start from a stationary position, engines are started and the rocket slowly gain acceleration upwards, eventually reaching orbit.
What I'm thinking is that the rocket "wastes" a few seconds reaching a speed/acceleration that could be gained by other means. That would save a little bit of fuel, but most importantly, it would mean the rocket leaves altitude zero at already some speed, making it easier/faster/cheaper to reach the final orbital speed it needs.
I'm thinking for example of a hole in the ground, a few hundred meters deep. You start the engines, then accelerate the rocket up until it reaches a speed of say 40km/h when at ground level, from where the rocket just continues with acceleration but already at an advantage. 40km/h doesn't sound like much, but by looking at rocket launch videos, they do take their time to reach that.
I understand it would be expensive to build such a mechanism, but it's a one time thing. I also understand that the calculations would be different, but again it would be a "somewhat" one time thing: once you figure it out, it's way easier to redo.
Am I subestimating these costs and complexities? If not, what would be the reason not to do something like that?
Note: this is cross-posted from Physics because I can't close the same post there, but it is about to be closed by members. Check the comments there.