A previous rejection does not permanently close the door. Firms reinterview candidates all the time after the recommended waiting period, especially when the candidate has built a stronger profile or clearly addressed the issues that held them back before.
The earlier outcome may still be visible internally, so you should not approach the new application as if nothing happened. The useful question is what has changed: stronger work experience, a promotion, better case performance, a new degree, or clearer evidence that you are now operating at a higher level.
If you were given specific feedback, use it. If the feedback was vague, reconstruct the likely weak points from the interview and get independent feedback from strong practice partners before you reapply.
The cool-off period is not just time you have to wait. It is time you should use to create a meaningfully better candidacy. If you come back with the same profile and the same interview weaknesses, the second attempt is unlikely to feel different. A useful reference is reapplying to consulting firms after rejection.