I was reading this article from NASA about chemical rockets and they argue that, with a planet 50% larger than the Earth (assuming similar density, about 1.5G surface gravity), it would be impossible for chemical rockets to escape. Note that I don't care specifically about those exact values, just assume a planet slightly too big for chemical propulsion to be able to power a rocket to escape. If people were stranded on a planet like this, how would they build a means of leaving this planet.
Assume that they have no help from anyone already in orbit, so they have to get to space on their own, and a planet otherwise similar to Earth. They can know as much or as little about our spaceflight technology as is convenient for the answer.
Also, all answers must be feasible according to our current understanding of physics. Anti-gravity devices, portals, and the like are disallowed, though far-future tech can be used if/where needed.