Did Flight Engineers progress to be pilots? When 3 man cockpits were common place on commercial aircraft what was the career progression of a Flight Engineer like?

Did FE's normally transition to be pilots? I'm not trying to insinuate here that FE's were in anyway inferior to the pilots and of course some FE's would of had no desire to transition to a pilot capacity at all.

Were there any airlines who operated a policy of starting flight crew out as a FE then training them as pilots?

N.B - Some background information that I'm basing this question on is I've read a number of reports regarding young (early 20 y/o FE's becoming pilots) and in maybe a more extreme case the hijacking of FedEx Flight 705 when the FE who hijacked the aircraft (an ex-Naxy pilot) had been made a FE (this could be part due to the fact he apparently falsified his Navy flying hours).
Before the turn of the century (I can't believe I'm using that phrase, as I retired in 1999) and especially back when all 3 engine and 4 engine airliners had a flight engineer, the usual career path at many airlines was to hire in as an Flight Engineer, or FE (two stripes), progress to an First Officer, or FO (three stripes), and then become a captain (four stripes).

This all began to change, of course, with the advent of large 2-man cockpit aircraft. The change was not without controversy and some pain. For example, at least one initial operator of the 737 ran a 3-man cockpit for a time. The 3rd guy was, as I remember, referred to as the GIB (guy in back). He sat in the jumpseat and read the checklists, which was one of the tasks an FE typically had in 3-man cockpits.

As it happened, the two jet carriers I worked for hired pilots into the FO seat and used professional FEs. I spent a couple of years on the 727 and then 10 years on the 747.  During that time, every FE save one that I flew with was ex-military, and with few exceptions all were A&amp;Ps. That was desirable in case a maintenance sign off was needed when you were someplace where maintenance was not otherwise available.

Occasionally you would encounter an FE who had been a captain.  The pilots were required to retire at 60 back then, but FEs weren't.  I only knew one such individual, and I always liked flying with him.  The more expertise you have in the cockpit, the better.

In the two 747 carriers I worked for, an FE would sometimes transition to the FO seat, but that was relatively rare, and the costs were typically the individual's to bear.  Interestingly, when I retired in 1999, I had flown with an ex-military FE who years later became the chief pilot of the airline involved.