I got really lucky, several times.
My senior year of college, all I wanted to do was keep going to Williams. I wasn't excited about - or even really thinking about - a career. Now, when undergrads contact me asking what working in product is like, I'm happily amazed at how much more capable and mature they are than I ever was.
I went to law school because the career counseling office didn't have much else to recommend to a philosophy major. When I got to law school, I missed my college friends, and I never got engaged with the material or new classmates.
I dropped out of law school and went to work for Forrester Research, mostly because few college friends worked there, and Forrester would hire people fresh out of college who weren't sure what else to do. I learned about customer research, data analysis, writing, business processes, and the tech industry, without really intending to. This was extremely lucky!
It was at Forrester where I learned about the role of product management and started thinking about pursuing it. I moved to an internal team doing a mix of training and internal product management for Forrester's research and consulting practices, just to get some semblance of relevant experience. I also moved to San Francisco while still working for Forrester. Most companies wouldn't have been so accommodating. This was extremely lucky!
When I started looking in earnest for software product management jobs in SF, I talked to a family friend who was a technical recruiter. She delivered the tough news that I wasn't likely to find a PM role, because I didn't have a comp sci background or an MBA. She recommended I timebox my search and be ready with backup plans.
A week later, I happened to have lunch with a high school friend visiting from out of town. Her boyfriend lived in SF, was a product manager at a company hiring entry level product managers, and he was willing to refer me. This was extremely lucky!
My resume was pretty light, so I'd put my LSAT score on it. The hiring manager happened to be dating an attorney, so - unlike nearly everyone - he happened to know what a pretty good LSAT score was, and figured he'd give me an interview despite my lack of directly relevant experience or skills. This was extremely lucky!
I did well enough in my interviews to get the job, and I've loved being a PM ever since.