I'd estimate a week? That's probably what you meant by "eons". :-)
It could go faster, but if we need to buy a new (expensive) network switch that can take a few days to arrive. And as you mention, the datacenter guys are happiest if you give them 3 - 4 days and a work order to do the cross connect.
Building out more vaults (the blocks of 20 storage pods we store data in) is usually about the same if we rush it, but we have a big (multi-petabyte) buffer spinning ready to accept data at anytime. We have a regularly scheduled delivery of pods once per month based on projections, but we have been known to tell our provider to go ahead and build three months worth of pod chassis (everything except for the drives) immediately and ship them to us. We supply the hard drives, so that either comes from our own stashes or we quickly order some more from various sources.