Hey, just as an update, probably useful for next round/year:
I got an email telling me I was selected to interview on the 4th in the night. That is 13 days to the notification deadline. It is really true what they say that they can call you at any time during the application process.
Also, since there was no availability for interviewing with an alumni they told me to do the pre recorded interview. The process is very similar to the Kellogg video essays, but a little bit longer (45 s to prepare, 3 minutes to answer).