It's a sad reflection of the current industry that Flight Test, like this forum, is a very small community. It has been said, only half in jest, that if you haven't got several mutual acquaintances (if not friends), then someone's lying about their resume.
One possible advantage for new entrants is that, as the Design departments are also fairly small, if you join the general Engineering faculty and do want to go into Flight Test then taking the initiative to, for example, help write the Certification Test Plan and all the myriad Functional Test Procedures (Rig, Ground & Flight Test) will probably get you flight testing and eventually into Flight Test.