Technically, mine isn't a "route to being an FTE/TP" - since I'm neither - but I have spent too many hours "flight testing" to not want to comment.
Basically, if what you want is to be "involved" in flight testing it doesn't necessarily mean you're flying; if getting airborne isn't the goal, then there are FAR more people involved in a test team firmly anchored to the ground, which means that for someone looking to get involved, it might be a bit easier to start off as an engineer (design/development type) and then develop (regress!
) into an FTE type role. Many companies second staff from the 'pure' engineering departments to flight test teams, and it would be possible to drift into a more permanent role there if you played your crads right. It's probably not a plausible role to TP - since you need to make two career changes, which is going to eat up time - but its very plausible for FTE, we've had guys do it. If you went that route I'd be tempted to advise going for a systems engineering role at first, because structural guys have very few reasons to do flight testing, their stuff is invariable rig tested, and because the basic FTE training will probably be weaker on systems than on aero, so if the company is looking to "fill a spot" its more likely to be for someone to specialise in the systems stuff. But that's just an opinion ...
Any, FWIW, my career path was:
* Maths degree followed by 1 year MSc
* 9 years at 'Scruggs Aerospace' as an aerodynamicist - where we didn't get involved much directly in testing, since the Flight Test group were very self-sufficient (or 'insular', depending on your POV!)
* 9 years and counting in Canada, again as an aerodynamicist (which they call 'flight scientist' here of course) but this time far more involved in flight testing, spending 3 of those 9 years in close proximity to ICT_SLB and a few others. I never actually went airborne, but several of my colleagues did (when, say, testing for ice and suchlike) and I've been on production test flights for troubleshooting since.
If I were to pick a single trait that will bring you success...
be flexible. The chances of the 'ideal' opening being available at any given time is small; for my own case, I've never worked in the discipline for which my MSc was ostensible preparation; my first company reassigned me to a different job to the one they had planned for me before I showed up. My company change was actually to a subtly different discipline; I got involved in the flight test teams by accident, or circumstance, twice. If I'd ever said "no, my career plan says I want to do X" I'd never have got where I am - though thats not to say having a plan is bad.