I've always been curious as to how effective a hydraulic lift could be at reducing necessary launch weight. A disproportionate amount of fuel is used at the beginning of the first stage when it is the heaviest, so seems like the benefit would be quadratic - Saturn V took 12 seconds to clear the tower. Would require major infrastructure, but if you could "throw" the rocket so it starts at a greater initial speed, seems like you could bend the rocket equation favorably. Perhaps even a giant underground potato-canon or railgun.
I suppose you'd be able to approximate the effect by comparing the delta v needed to launch from a sea-level site (Cape Canaveral, Kourou, etc.) with that needed to launch from one of China's inland sites (e.g., Taiyuan, which sits at 1500m). I have no idea whether this data is publically available, though. I'd guess the bulk of your performance improvements would come from increased engine performance due to the lower ambient pressure (~0.83 atm according to Wolfram Alpha) rather than the increased altitude, since most of the energy is needed for horizontal acceleration [0]. The increased thrust would mean lower gravity losses, but I wouldn't be able to say how much.
https://www.nasa.gov/topics/technology/features/horizontalla...
So far all demonstrations have been of rockets mounted under a jet engine powered aircraft, which then detaches at space launch. But I don't think there is any reason why you couldn't have a SSTO air/spacecraft, other than we don't have the propulsion technology yet - it works in KSP though :-)