Transition from solid MM to BB? how long?

I recently was offered a FT IB analyst position at a pretty solid MM shop (think Jefferies, Friedman Billings)in NYC and am pretty happy with the position....however I do want to make the jump to a "mega fund" PE shop in next 3-6 years after doing banking. I realize that you need to be at a top 5-7 BB or elite boutique (ie. evercore) to go to a Blackstone/KKR/Cerberus etc.; how hard is it to make the jump from a MM to top BB or evercore...after 8-16 months at the MM shop? Thanks for advice.

FYI: My offer was a generalist, but I plan to go into either M&A group or Fin Sponsors/Lev Fin, not industry coverage