We just got back from the embassy, let me explain the process.
Our appointment was scheduled at 10:30. My wife and I and baby arrived at the front of the embassy at 10:15. We went straight up to the blue window for USA citizens, which is the first window on the left. I call it the blue window because all the visa Windows have yellow numbers above the window and this window has a blue sign above that says us citizens, pretty straight forward. We handed in our appointment acceptance email.
We entered the embassy and entered the big waiting room. They told us window 17. We had to take a number for us citizen services, the numbers are near the front of the room in front of booth 16. There are two rolls of numbers but one is for services and the other is for notary or something else, if you have any questions just ask the other people. We waited for about an hour, several people were in front of us who had lost their passports. We finally were called to window/booth 17. They asked for all the paperwork found in the checklist and we handed everything in. If you have everything in order and filled out, everything should be ok. They asked for evidence and I turned over high school and university transcripts and my old passport.
We then went back to the waiting room and waited for them to call us by name, after another thirty minutes they called us to booth 12. I paid the fees and then we waited again. After another wait they called us to booth 16. The embassy worker reviewed all our paperwork, we then signed a couple of forms, swore an oath and he said we were good to go for our Babies passport, CRBA, and SSN. We turned in the DHL waybill that we bought last week and he said you will receive everything in two to three weeks. I asked does that mean we will have in hand everything in two to three weeks and he said yes.
So to answer your original question, two to three weeks. Just some advice, the worker was happy that I filled out a detailed history of my time in the USA. He said a lot of people don't do that, and it helps to be as detailed as possible with as much evidence as possible.
We plan on flying during the week of the 13th, in four weeks, but I imagine we could travel a week earlier.
Good luck