Why not build a space elevator starting from the moon?
Anchor one end of the cable to the side of the moon that faces the earth. Drop the other end of the cable to earth so that it drags along the ground. The earth's gravity and friction contributes a degree of tension to the cable. As the earth does its daily rotation and the moon does its monthly orbit the cable drags around, flicking over mountains and knocking over buildings.
Because the earth's rotation and moon's orbit happen on different planes with different periods, it never goes to the same place twice. Everyone within 30.12 degrees of the equator (the earth's axial tilt plus the moon's orbital inclination) eventually gets access to the space elevator whilst simultaneously having their cities destroyed.
People build carriages to intercept and attach to the rogue elevator cable and ascend into space.
Problem?
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1 answer
Problem?
Well, I think you stated the problem pretty well already in your question.
As the earth does its daily rotation and the moon does its monthly orbit the cable drags around, flicking over mountains and knocking over buildings.
and
Everyone within 30.12 degrees of the equator ... eventually ... having their cities destroyed.
Even without looking up the numbers, I can tell that this would work out to a significant fraction of the Earth's population. I wouldn't be the least bit surprised if, even with today's population and distribution, we are talking about anywhere between one billion and three billion people.
Seriously, why would anyone want to do that? And like WhatRoughBeast pointed out, the cable will be moving across the ground at approximately fighter jet aircraft speeds. Add to that the continual sonic boom produced which will wreak havoc (and drastically lower property values) in the vicinity as well.
When I saw the question title, I thought your question was "hmm, we can't build a space elevator on Earth, but maybe we could do it on the Moon, with its much lower gravity?". (The answer to that, of course, besides all the issues with, you know, actually building the thing, is that having a space elevator on the Moon wouldn't really do anything at all to make access to space from Earth any easier. We'd still have to climb out of Earth's gravity well.) But turns out that's not your question at all.
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