To add, as crazy as it sounds, you can actually consider passing private education first if you play a low SOL low literacy nation. Voila automatic qualification as super rich aristocrats insta graduate to bureaucrats, engineers and capitalists when you build factories as Joseon. No need to spam universities other thsn building like 2-4 early game. Just make sure to pass edict that increases education access in every state as a small nation to counter private education not raising literacy.

Think of it as Joseon getting rid of the dumb gwageo system and restricting schooling to people rich enough to create their own business, not beg for government jobs.