Transition from Big 4 to BB IB?

Hey All,

I am currently a freshman student at a non-target school for IB, however 2 of the the Big 4 firms as well as many other consulting firms come on campus to recruit for internships and full time gigs. I was wondering if I supposedly got a job in Transaction Services/Advisory for the Big 4 and did a couple years there and then got an MBA, would I be able to make the move to a BB IB?

Thanks