Last year our DS heard back on his first nomination 12 days after the interview via email from his MOC's secretary, this was followed by a posting on their web site listing all of his Service Academy nominees. Then his portal updated showing the nomination 2 days later. Another week later he received certificates for both nominations received in a decorative sleeve. This was a very nice touch.
Another MOC sent out acceptance/rejection letters 3 weeks after the interviews and he did not receive a nomination that time. We never heard back from another MOC after the interview process, but he actually received a USMMA nomination that he never asked for from this MOC. The MOC's secretary had called my DS prior to the interview and asked if he was only interested in WP and USAFA or if he would consider the other academies. He said he was open to all possibilities. A month later he got a message from USMMA saying he had received a nomination and he needed to start the admission process.
This year he interviewed with the first MOC's same panel last Saturday. His field adviser emailed this morning and said he had the nomination and to hurry and complete his CFA since that was his last piece of the puzzle. His portal has already updated showing the nomination. He still has not received the official message from the MOC or his office though. So in our experiences.... it can happen in less than 48 hours or take a month.
FYI, DS is reapplying after not getting accepted last year. After he received his TWE in April, he was granted a full AROTC scholarship that he never applied for. They reached out to him with the offer totally out of the blue. He has enjoyed being a part of the AROTC but he really wants West Point.
The service academy appointment experience is a wild crazy roller coaster ride.