Recently, I have been seeing a number of posts on undergrads starting out with back office type jobs and seeing what you can do to advance yourself to the client facing side of the business. What follows below is strictly for those who have been able to score only BO/MO roles at BBs who eventually want to be in FO positions.
Having worked five years at a BB in a BO/MO role, I have seen several ways that people break into front office roles. Networking within the unit that you support. It is quite possible to break into a front office role of the unit that you are directly supporting. There have been people that I have seen break through to work on the business side after working in the BO. Although this is rare, it is possible, it requires being a top support analyst who has a good relationship with the desk, is usually able to break in after spending at least two years in the support role. Most people with this approach will most likely fail during any interview process, but I have seen enough successful cases to say that with the proper preparation, it is possible.