You could build something like maglev train, with no drag from air it would not find too hard to hit needed 2.48km/s to leave moon.
No giant springs or such, you would die from not-so-small acceleration. You would need around 1.5 minute of acceleration at ~3G and 95km and 48s and 47km at ~5G, so that human can survive.
For sure, we are sane people and wont be sending trains to Earth only delivery vehicle. Something close to what we use now for atmospheric entry: capsule, shuttle.