All those co-ops and apprenticeships require connections.
Not true, at least in Canada. I did a co-op Engineering program and our university had a dedicated co-op department whose sole task was to line up work for students. It was very successful; pretty much everyone was employed during every co-op term in my class. And these were real, paying jobs, not unpaid internships.
Doing co-op meant my program took 5 years instead of 4, but it was well worth it. I graduated with 24 months' of actual work experience and no debt. Granted, this was quite a while ago when employment conditions were better, but even now co-op students do relatively well.