How do you get a referral when you don't know a single person at the company?

Everyone says referrals are the way in, and I believe it, but I don't have a network. I'm self-taught, no alumni connections at these places, no former coworkers in tech. So 'just ask for a referral' feels like it assumes I already have people.

Do you cold-message engineers on LinkedIn? Does that ever actually work without being weird? What do you even say to someone who's never met you? Would love to hear how people with no starting network broke in.