Early on in my career, when I began to get interested in project management, I started looking for problems that needed solving. At the time, I was working for UTHealth, at the School of Public Health. During my tenure with the university, I began to sense the need for a URL shortening service that was branded. Because multiple schools and marketing departments were interested, I took this on as my first real "project".
I spoke with interested parties to get an idea what they needed. In addition, I worked with database engineers, infrastructure administrators, and designers to end up with the product that we needed.
I wrote the application, working with input from all the stakeholders mentioned above. And for my first real project, it was a wild success; the application is still in use to this day!
The reason that I mention this project, it that it created an appetite in me to make a career of this. Not just engineering, but real project/product management.