ok lets say you were going gto build a space elevator

would you drop the cable down or try to push it up to be captured by a passing satellite?

if you dropped the cable down from the satellite you could fire the thing downwards towards the earth by rocket whilst over the equator

maybe at first you’d have a huge cable drum in orbit so it could be dropped all at once maybe you’d need a special weight at the bottom of the cable to counter the winds it would encounter, maybe it would have its own power source or a jet engine to resist winds trying to push the cable this way and that it might be a funny looking cross wing device with the engine in the middle?

maybe you’d have something like a scramjet device to power the thing downwards quickly??

whatever the cable was made from would have to be strong

something i was watching suggested that power would have to be passed through it to power the elevator upwards ie the elevator grips the cable and moves upwards

maybe once one cable had been placed you’d strengthen it with more so that it was a much stronger cable

a device might travel up and down the cables fastening them together?

Drop it down.
Not very likely to happen here on Earth as we can’t make anything strong enough to work commercially, nor are likely to with any foreseeable technology.
We can make carbon nanotube that’s just>i? strong enough, but that doesn’t allow for enough safety factor.