How to Break Into the News Business Without a Journalism Degree

Every single job listing I see in the news Biz requires either a journalism degree, two to five years of journalism experience or some combination thereof. How do non-trained journalists nowadays typically break into the news business if they have a background in say science? Is it just about having the right connections? What outlets are still willing to invest time in training new reporters? Do you just have to successfully pitch enough freelance pieces to build up a portfolio? I consider paying to learn theory rather than being paid to learn on the job to be a scam. And we can debate later where to get chicken wings now because everybody knows the anchor is over.