I believe carbon nanotubes are barely strong enough in theory - so you just have to make a cable of a reasonable thickness out of them long enough to reach past geostationary orbit without any flaws in any of the nanotubes that make it up - each of which has to reach the entire way. Currently I think we can probably produce them in lengths of maybe as much as a foot? Probably less, maybe much less.

And then you have to make sure there’s no issues with it, as it falling down would cause a global catastrophe.

They’d actually be much easier to build on the Moon or Mars, and could be very useful there.