Even if it takes a decade or two, the smaller nations should and I believe will support Japan or Korea or Turkey to develop engines, jointly if possible, because the countries that currently produce engines, the technology is always selectively available and best ones are never available.
Korea and Turkey are not currently going for immediate engine development, they know it is beyond their ability, KAI-KFX and TAI-TFX are mainly for air frame, avionics and weapons system development. They were planning to use US or European engines from the start.
Japanese ATD-X (Shinshin) program does include a plan to use indigenous engine, IHI XF5-1:
http://www.mod.go.jp/trdi/research/gaibuhyouka/pdf/XF5-H21.pdf
The engine in this pdf file has thrust of around 50 kN, which is similar to Snecma M88 of France used in Rafale.
Another variant of this turbo-fan:
IHI Corporation F7 - Wikipedia, the free encyclopedia
is being used in this Maritime Patrol Aircraft Kawasaki P-1, entirely made in Japan:
Kawasaki P-1 - Wikipedia, the free encyclopedia
test flight of test model XP-1:
https://www.youtube.com/watch?v=6dQIxiXNilk
production model P-1:
https://www.youtube.com/watch?v=vwgAcuRn-DU
https://www.youtube.com/watch?v=TUGt8FbyxM8
Now all of this nothing compared to even China, let alone Russia, Western Europe or USA, but its a good start and it shows that they have potential, if they can line up support from other nations, of course after getting rid of their moronic weapons export restriction in their constitution.