I understand the situation you're in. People always say that if the first person you talk to is in HR, you're already screwed. Or another version: if you just submit a resume through an online platform, you're screwed.
I haven't done it myself, but I've seen friends break free of this. The best, most difficult, most time-consuming way is, of course, to meet lots of people. You never know who has a connection where. Opportunities come from surprising places.
A much quicker hack is to send messages on LinkedIn. Find the person who would be your boss at the company, tell them how much you like the company/product, and ask them if you can buy them lunch and learn more about their team.
In some cities/cultures, like NYC, this almost never works. People are really busy. In other places, I've seen success rates as high as 10%. Of these, around 25% seem to result in offers (assuming the person is qualified for the job). That's not bad!
In general, it's (unfortunately) going to take a lot of footwork and rejection.