Big Four Deal Advisory --> M7 MBA --> PE or VC. Possible or am I being overly optimistic?

I'm currently at a good non-target university (One of the UCs, but not UCLA or UCB) with a job offer to go full time at a Big Four firm in Deal Advisory in the Bay Area. I'm viewing Deal Advisory as a chance to learn FDD and improve my resume for a few years before potentially applying to grad school and transferring into PE or VC.

Do I have a chance to get accepted to a M7MBA program? I interview well, have a 3.8 undergrad GPA and expect that I'd do fairly well on the GMAT (99th percentile on SAT).

If I were to get accepted to a M7 program, would it be feasible to transition into PE or VC?

My goal here is to get into PE or VC without first having to do IB. How feasible is this plan?