in order to properly prepare for a case interview you should mainly work on the following:
- Define a calendar on how to prepare
- Learn the basic frameworks/theory for cases
- Learn how to answer to the fit part (including your questions at the end for the interview)
- Learn how to answer to market sizing questions
- Practice math and graph analysis
- Read examples of cases
- Practice the cases, fit and communication skills live
Starting from zero, it is likely this will take 150-200 hours. Thus, either you are able to put 8-10 hours per day starting from today, or you would have to reschedule, as already suggested. Ideally, you want to first check which day you should have completed the preparation with the previous amount of hours/activities, and then suggest to have the interview after that day, in order not to risk to have to postpone again.
As for potential resources to use in the various steps, you can find a list at the following link:
As a side point, it would be very risky to do all the preparation focusing on one firm only; to maximize your chances to land an offer, at the bare minimum it would make sense to apply for all MBB companies; moreover, even if you are interested in MBB only, it could be a good idea to consider other consulting firms as well, since this could bring you to MBB in the long term (I know several people who joined MBB after a couple of years in RB, OW, ATK etc). Adding additional companies to your list would of course imply some more hours to be added to the previous estimated amount.
Hope this helps,