Hey! Happy to share how I've been nerd-ing out over this! So I've been looking at timelines here on VisaJourney, particularly people's NOA2 dates and NVC receive dates. I also looked for dates that people got their NVC case numbers. The pattern shows that, recently, cases have often (not always) been sent out around roughly 3 months after the NOA2 and around roughly 3 weeks after NVC case creation. This does vary, of course.
Then I looked at the calendar of dates the NVC supposedly ships cases to embassies, which I got from the Facebook group for "July & August 2021 K1 Visa Filers".
February 14, the next shipping date, seems to line up with my timeline based on the stats I mentioned above. (My NOA2 is 11/14 and NVC case creation date was 1/21.) I know that this is not a guarantee and things can always change, but it does give me some idea of when I might be able to expect my case to be sent out.
Although it's not certain, hope it helps!