We had roughly the same youth unemployment in Spain at the peak of the 2008 crisis. The problem was not education.
More like you need a business friendly environment with low taxes, minimal corruption and frictionless bureocracy to create a thriving local economy and also attract external investors.
You can also be a wealthly petrostate (with or without corruption), or a corrupt, dirt-poor state with no labor laws and be booming with outsourced low-wage textile jobs, or a command-economy with plenty of pointless make-work jobs...
If your goal is just to have a lot of jobs to keep your young people busy so they don't foment a revolution, there's plenty of ways to go.
I think the crisis was kind of exceptional as everyone was going to be pretty screwed either way. But furthermore, it seems that until you reach a sort of 'critical mass' of educated workers it can be hard for them to find employment as it's hard for the country to attract companies that require an educated workforce.
I think the solution would be to continue investing in education to help reach that critical mass and at the same time make it easier for people to set up new companies, start-ups etc.
Spain is pretty bad for this with the harsh autonomo taxes for people trying to start their own business etc., plus all the bureaucracy which often has to be done in-person and appointments are hard to get etc.
At least it seems like things are improving, although the Coronavirus will be a setback.
[1] https://www.euroweeklynews.com/2020/11/13/spain-has-highest-...