They had to design the software, the UX including the touch wheel, the mac integration and syncing, and everything relating to the design, materials, and sourcing of the components. It’s astonishing that they got it done in less than a year. (And I highly recommend Fadell’s book)
The iPod's OS was bought off the shelf. All of the music library functionality and a lot of the sync functionality already existed within SoundJa...iTunes.
That's not to knock the speed of the iPod's development but it wasn't built totally from scratch. Apple also wasn't a garage startup, peeling some hardware engineers off for the iPod wasn't going to cripple the iMac's continued development.
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?
Most inventions become trivial right after they are released. Creation, research, design are the hard parts, and you cannot judge those by the complexity of the final product.