Given the ages that the students sit the exams and their similarities to the current UK system
GCSE = OWLs (good grades needed to stay on to NEWTs) - trade apprenticeships can be entered here (carpentry etc)
A-Levels = NEWTs (Good grades needed to get into the apprenticeship or career you want)

And then apprenticeships in potions/charms (Apprentice/Journeyman/Master) etc to be the equivalent of research degrees (Bachelor/Masters/Phd). Since the exam curiculum wouldn't leave much space for ranging academic research. I'd presume it's also why you can't become a professor straight out of school, you'd need more experience and expertise than that offered by Hogwarts

I always figured this because third level academic qualifications were meant to be apprenticeships in 'thought and research' (its why every PhD is a doctorate of philosophy regardless of subject) So I am a Doctor of Philosophy, even though my subject is the law

So you either go into a profession and get on the job training/qualification through doing (like doctor and lawyers did then, and still sort of do now), or do an apprenticeship in a research discipline and move through the ranks of apprentice, journeyman, master the same way other apprentices of the period (and today) do.