In the US, many Professional Flight Engineers started out as Crew Chiefs or Flight Engineers in military transport airplanes that required them.
There are still a few airlines (mostly cargo carriers) that hire PFEs, but the number of jobs is steadily decreasing as the DC-8s, 727s, DC-10s, and 747-200s are being replaced by 757s, 767s, and 747-400s.
Virtually all the passenger airlines that have 3-crew airplanes hire Pilot- and FE-qualified "Second Officers" to fill the FE seat as an entry-level position. Most of those bid up to higher-paying First Officer seats as soon as possible.