I don't know if things have changed since, I had my interview back in 2016, so quite a few years ago.
Back then, and possibly still, they only held K-1 interviews on Thursdays, and there was only two slots each Thursday. So yeah, the wait time can potentially be long depending on how many applied around the same time as you. I messaged NVC and got my case number about 30 days after my NOA2, that way I didn't have to sit around and wait for the NVC letter that took way too long to show up. The case number is not needed to book a medical, but you need it when you go to the appointment.
I got my NOA2 in the end of June and managed to schedule an interview for the end of August, so that wasn't too bad.