When we did our daughter's German passport, it took like ten minutes at the Rathaus. No problem period and it wasn't that expensive either. I have no idea why in the world you just wouldn't do the passport in Germany instead of messing with it later in the US.
I have to admit, I like using it already to pick and choose the shorter immigration lines in the EU.

Oh, and, yeah, you both have to be there, the father and mother. The baby has to be present to be presented to the CO. It didn't take long for the passport to arrive, but the SSN took the better part of three months.