First off, remember that everyone's journey is different, so don't be too hard on yourself for feeling "behind" in life. It sounds like you're on an upward trajectory and that's what's important.
To improve your chances of landing an interview, here are a few strategies:
1. Improve your resume and cover letter: Your GPA may not be perfect, but there are other ways to showcase your abilities. Highlight your achievements, experiences, and skills relevant to consulting in your resume and cover letter. Be sure to also emphasize your upward GPA trend in your master's program.
2. Leverage your network: You mentioned you have connections at Oliver Wyman, Strategy&, and Kearney - that's a great start! Referrals can significantly increase your chances of landing an interview, so don't hesitate to reach out to these contacts when you're ready to apply.
3. Gain relevant work experience: Your idea of gaining experience as a functional consultant at Murex is a solid plan. Such experience will not only make you a more attractive candidate but will also provide valuable insights and skills that you can bring into your consulting role.
4. Showcase your problem-solving skills: Consulting firms, especially MBB, value candidates with strong problem-solving skills. Highlight your analytical, numerical, and strategic thinking abilities in your applications and any preliminary assessments.
5. Practice case interviews: Your concern about preparing for interviews is completely valid. One way to alleviate this worry is to start preparing now. Practice as many case interviews as you can and consider getting a case interview coach to guide your preparation.
Finally, remember that the path to MBB isn't the only route to a fulfilling and successful career in consulting. There are many other reputable firms where you can develop a fruitful career.
Keep your chin up, and keep pushing forward. It's not a matter of being behind in life; it's about making the most of the opportunities that come your way from now on. You've got this!