The machine that does this first has to leave Earth and land softly on the moon before it can start boosting stuff back. You can’t skip the first two steps.

Not quite.

The machine that does this needs to be built by a machine that is carried by the machine that is first built and launched from earth before you can start boosting stuff back.

It is feasible to build a space elevator on the moon with existing materials.

You could build a railgun on the moon and launch stuff back to earth.