Another tack
One way to blast through the gate is to offer your first piece to a magazine pro bono. This is different from "on spec," where you get paid if the editor accepts it. Pro bono is just what it says: fr*e.
I wouldn't do this for big-name consumer magazines, where you're lucky to get published every year or two -- if at all. But for regional publications, trade and business journals, or any magazine that pays fairly and is a good prospect for frequent work, it might be worth it.
The only time you'd do this is when you want to craft a relationship with the editor for REGULAR, REPEAT assignments (at your regular, fair rate).
Your first article is the only reliable way the editor can get a feel for whether you'll work out as a writer for their mag. Your past experience and education are far less important than what you can provide to them now, and the only way to show is to do.
If your first article is good, the editor won't care about your past experience (or "lack" of it). All that matters is whether you can write well, now ... for them.
- Michael
P.S. - Some writers get rabid about being paid for everything they write. That's fine. We're not talking about "writing for fr*e." Think of it as the cost of marketing in order to land a lucrative, long-term client.