If you front-load the cost of a mostly-automatable construction of a space elevator (factory in orbit spitting out woven carbon nanotubes in opposite direction like a spider's spinnerets - this is almost definitely wandering into the realm of sci-fi, but maybe?), synthesizing the manufacturing components and launching them to orbit will be the most difficult part.

And if we can refine those materials from asteroids, that cuts the resource extraction cost as well - no need to ship it to orbit. (besides, what if the manufacturing technique for said carbon nanotube ropes require a weightless environment?)

There's even research into using the earth's magnetic field to generate electric potential this way.

Then of course there's the collision and weather and so on and so forth.