Laser propulsion is thought to be a better way for launching from the Earth, and has been tried with small models. You build a powerful laser ground laser system, and through some method I'm not clear on, heat air in pulses? in the bell of the rocket chamber. Once that gets too thin, the top layer of the chamber is ablated to provide the final thrust needed.

Supposedly can be gentle enough for humans, see some of Jerry Pournelle's fiction and non-fiction for examples of this.

Or, if you're in a hurry, there's always Orion (see Niven and Pournelle's Footfall): https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls...