There's a lot of alternatives, the main constraint is that it has to be built from the ground up, so space elevators are out.

I think a dynamic structure such as a launch loop https://en.wikipedia.org/wiki/Launch_loop would work.

Also inflatable towers for launch assist https://en.wikipedia.org/wiki/ThothX_Tower

For even kookier options we've got lasers! https://en.wikipedia.org/wiki/Laser_propulsion https://en.wikipedia.org/wiki/Beam-powered_propulsion