What kind of companies are you trying to work at? I totally feel your pain. In fact many ATS's (Applicant Tracking Systems) often bounce 50% of applications without a human even looking at the app.
Hiring is hard on both sides. Many companies (understandably) need some way of filtering. That's why you shouldn't apply online or through job portals =)
The CTO of Stripe talks here about how he built a great eng team: https://www.youtube.com/watch?v=3Zoq085zVhA
you can see that most are referrals vs. in-bound leads, with other channels in between.
What I'm getting at is that regardless of industry, you should do some of the following:
- contribute to the field you're applying to in other ways. Write articles, do side projects, etc. This will build up your reputation and experience in ways that a company can substitute a degree for.
- find people in the field and talk to them about what they're doing and what they'd find most helpful to study up on.
- take an internship or research position
- find people at LinkedIn who work at the company and meet up for coffee. Companies are definitely more amenable these days to hiring non-degree candidates but HR might be a bit behind the times. If you can demonstrate to hiring managers directly in-person that you're qualified, you can bypass a lot of these issues
- apply to startups / smaller companies. it's more of a meritocracy for sure and HR tends to be more hands-on.
good luck!