You do not need a degree to get publishing deals. You are judged on one or both of these things: (1) the quality of your writing (this one is optional as you'll see from the next paragraph) and (2) your author platform, which is how many thousands of engaged followers you have on social media (not bots!), the size of your email marketing list, your connections, plus how much you are willing to spend on book marketing, etc.
You get an author platform by either: (1) becoming famous for something or (2) getting widely published (and read) online and in publications related to your genre. If you're famous but a crappy writer, you can hire a co-author.
If you have those two things, the next step is to interest a legitimate literary agent in your work. The agent works to get you the publishing deal and gets paid a commission when they sell your book to a publisher. Large legit publishers won't accept pitches or manuscripts directly from writers because, when they did that in the past, they would be lucky to find one publishable manuscript per 10,000 submissions. So they now rely on literary agents to be the gatekeepers.
Just watch out for scam agents who want to charge you a fee up front. They make their money from desperate writers, and don't have to sell anything new to publishers to make money (though they may have made publishing sales in the past).