It doesn't really work that way. "Web Dev" is not a job; it's a generic name for an industry that covers a multitude of different specific jobs, each with their own specific (and overlapping) skill sets, and all of which are a subset of the much larger "Software developer" industry.
I don't really have any advice here. My approach was learning to program computers and gradually building my skills from the ages of 12 to 26, including several paid part-time/temporary jobs towards the end. Then a friend asked me to leave graduate school and take a programming job at his company, to take over a project he didn't want to run. I took the slow road, and stumbled into the career on a whim. (I'm a Mechanical Engineer and thought I'd be building robots, with programming just being one of the tools of my job.)