Empirical evidence proved it is more difficult to design and build aircraft engines than it is to build atomic bombs or send satellites to space. The jet engine is HARD.
It took many decades for US, British and French engine makers to perfect the technologies that they use today. China couldn't just acquire the plans and start making them. Creating turbine parts that can survive extreme heat has been a major engineering challenge. Meeting it has required fundamentally rethinking the material structure of the turbine blades, making metals do things that they do not normally do in nature. Turbine blades may be operating in temperatures far exceeding their melting point, and thus must be cooled to typically 85% of melting temperature to maintain integrity. Blades must be cast with intricate internal passages and surface hole patterns needed to channel and direct cooling air within and over their exterior surfaces.
The turbine blades in a modern jet are a single metal crystal. Even if you have a jet and can take it apart that tells you nothing about how to cast the turbine blades, and you can have a turbine blade that looks fine but self destructs after 200 hours. As an example, the load on a single turbine blade that's only 3 inches long can be as much as 35 TONS due to the centrifugal force on a turbine spinning at 20,000 rpm at temperatures over 1,100F. Only single crystal nickle-steel can sustain that kind of load for 2,000 hours without fail.
One of the biggest reasons why China is so lagging behind in jet engine is the Culture Revolution, which thousands of scientist/engineers were purged, thus created a talent gap which China took a generation to pick up. By the time China got its sanity back, it's already in the 1970s. Chinese engines have to compete with mature jets already in the market place, and US and UK engines didn't. This let them make profit while they were making junky engines. China doesn't have that luxury.
China has been making jet engines for decades, starting with WP-5 in 1956, which is a licensed copy of Soviet VK-1, which itself a knock-off from Rolls Royce Nene. China and UK signed a license deal in 1974 for the Rolls Royce Spey engine, but since UK committed to transfer technology, but not manufacturing know-how, by the time China overcame all the technical difficulties associated with manufacturing the jet engine, it was already mid-2003. China probably will surpass France by end of the 2020s, as China has multiple engine developments in the pipeline.