Some examples -- skyhooks -- large counterweighted swinging things that reach down into upper atmosphere and spin you right round baby right round -- a bunch of gravity assisted momentum ideas where you get the sun or the earth or what have you to get you really going, and then use that momentum to get a little thing up and moving more quickly. Space elevators -- hang a giant heavy thing out off one end, and drop a cable made of uninvented nanoscale tech down to earth, then just, you know, climb.

And then there's orbital construction, which requires some .. construction materials. The long standing idea has been to either go out to the asteroids and build there, or bring an asteroid or two here. Both have a lot of problems, and are a long way off. I think it's most likely that human governments will opt not to have the ability to make giant tungsten rods hanging over their countries, and will, to the extent moving an asteroid were ever viable, require they be a long way away, or alternately that we just go to the asteroids and construct elsewhere.

We are like maybe a century from all this being viable, and that's if companies like SpaceX keep moving at the clip they've been moving for that century.

Nobody lives there (within rounding error), and shipping in supplies to build rockets costs even more than launching from the ground.

Also we can do reusable launches to LEO so it's not all that inefficient.

You need the rocket to get to LEO or the moon. Once you're actually in LEO your propulsion system needs relatively little thrust, but you've replaced a moderately hard problem of launching from earth with a much bigger one of assembling things in orbit using material that's already there...

Assuming you mean getting materials from the moon, such as ice, the problems is that it would take 100s of billion in investment on the moon to do that practically. Everything from mining robots, transport and launch infrastructure. Plus infrastructure in LEO to refine that stuff.

If you do the math, assuming you have something like Starship, for those 100 billion to pay for itself, you likely would require an absolute absurd amount of materials from the moon. And on earth we have all the materials, refining capabilities and so on. Far, far cheaper to just launch it from earth in its final required form.

Unless you really want to build a fleet of inter-generational spaceship to explore the outersolar system, this is unlikely going to be make sense.

If you really, really want to transport stuff from the moon to LEO (for some reason), as long as it is basically ice, then its better to use some kind of mass accelerator.