Everything around the software would have been quick -- both the iPod UX and syncing were extremely simple back then. The iPod didn't really have a GUI, it was just six lines of text and a header line.
It's the manufacturing speed that astonishes me -- the sourcing as you say, the supply chains and the factory capacity. I'm also very curious about the manufacture of the scroll wheel -- was that something really new that had to be figured out (it seemed/felt like it) or was it a trivial combination of existing components?