Up at the top menu, when you click on "Departments", "Education", "Education Priorities", then click on "change professions", you get a screen that shows how many people are reserved and how many are needed for 100% production in all your companies.
Compare the two columns. You should find some entry in the 'reserved' column that is much lower - such as 'high tech engineers'.
From there, you can move a few people you don't need to low level workers and then beef up your universities a bit so you can produce more engineers - or whatever you're missing.
New players are constantly having to demote skilled but unemployed workers, and then re-educating them to something they need - it's perfectly normal.