Army Officer Seeking Advise on transition to PE

Hi everyone, I am a Field Artillery officer in the U.S. Army, graduated from West Point with a Mechanical Engineering degree and a GPA in roughly the top 25–35% of my class, and my Army commitment ends in May 2029. My long-term goal is private equity, and I’m currently deciding between Army → T15/M7 MBA → IB Associate → PE and Army → IB Analyst → PE. My concern with the MBA route is that I would enter IB around 29–30 as an Associate with essentially no finance experience and potentially recruit for PE around 31–33, while traditional candidates may have several years of IB experience by that point. On the other hand, my concern with going directly into IB is that my degree is Mechanical Engineering rather than Finance/Economics and I have no traditional finance background. If I pursue the direct-to-IB route, what should I do over the next three years—finance/accounting coursework, modeling programs, CFA Level I, veteran finance programs, internships/SkillBridge, networking, etc.—that would actually make me competitive? How much does a non-finance degree matter for IB recruiting if I can demonstrate strong financial modeling and finance knowledge? If I eventually want PE, would firms view a post-MBA IB Associate differently from a traditional IB Analyst with 2–3 years of experience, and is my age actually a meaningful disadvantage? Finally, is there a third pathway I’m overlooking, and if you were in my position, which route would you take?