To answer the "how quickly" part of your question, normally the nomination board will let the interviewees know around when they should release the nominations. For example, the senator I interviewed about 3 weeks ago will release his nominations in mid-December. Each senator/congressman will have a different timeline.
My DS had his virtual interview with our congressman's panel on 11/5 and he texted me at work on Monday 11/7 that he got the nomination. He had received an email from the staffer that he had received he nomination, and the official letter from the Congressman was attached. I think the nomination appeared in his portal later that day or the next day. We weren't expecting that kind of turnaround, so we hadn't even had time to play the waiting game . I was a nice surprise and relief!
DD found a Nomination in her USNA Portal on 11/17 after 10/22 Nomination Board Interview. After follow-up she found that Senator Rubio snail mailed the notice, which has not come yet.
This! There are 535 MOCs, hence up to 535 different ways to execute the nom process. It’s not YMMV. It’s “your mileage will vary.” So instead, focus on what you control.If/when/how they might contact applicants vary so there is no way to answer that question in general.