Yes, the analogy they use is to suspension bridges. First you shoot a string across your chasm, then you pull climbers with successively larger strings across it, until you get a size you like, and keep it.
The first strand would probably be on the scale of microns in diameter. you'd need to have some good skills in winding up string, Super bright LEDs and micro-sized radar, so that you can find your little micron strand floating to the ground. I think you could launch it on a single heavy lift rocket.
Hm, I didn't think about letting a string out upwardly for the anchor. You'd probably need the anchor to be reeled outward from your geosynch station. You might have a second launch with the anchor and far out string attached that docks with the string going back to earth. You can let out the anchor slowly as you get more laser powered climbers coming up from the ground, so that you keep its cg slightly past geo.
Hm, if we do a non-equatorial elevator, then the tapered ribbon is going to be flung down toward the equator asymptotically. The geosynch station would probably make a bump down in the shape with its increased mass. Anyway, the point is that the geosynch station wouldn't really be above the equator. Which means if you don't allow people out beyond the geosynch point, as I suggest, then you are going to be launching people out of a wierd orbit the aren't you?
That is where the distinction between geosynch and geostationary comes in handy. An elevator anchored off the equatorial plane would settle down to a kind of asymptotic line once it is built.