Someone had asked this elsewhere but then deleted their own post and I don't know why! I was meaning to come back to it and read it, so rest assured that I won't delete this one as there were some really interesting stories of unconventional ways people landed their work.
TL;DR: I got headhunted after directly emailing dozens of people and pitching myself as an available, on-call substitute in my line of work, instead of submitting job applications traditionally.
As for me, I cold-pitched myself via Google Maps and other searches as an available substitute to those in my skilled trade (upon moving to a different region) in basically a 50-mile radius, and eventually word of my availability reached a large, overarching institution that connected me with an organization that had a full-time opening. It took me probably 4-5 months from the move to the job offer.
Edit: My story is actually a little more complicated than that, now that I recall the details from years ago; there wasn't actually a full-time opening at my now-workplace at the time, haha. What happened was that I was briefly interviewed and quickly hired as an assistant to an overwhelmed director who ended up getting massively sick and nearly died from COVID, so I subbed as the director. They had been having interpersonal problems with her and I rapidly noticed them in the weeks before she got sick and warned them of her. While I wasn't trying to take her place, the higher-ups said they were aware of her shortcomings (she had basically said "Shut up" to another director higher than her rank, to give you one of many examples of how bad it was, and she must have been in her 50s if not 60s).
Nearly everyone at the org apparently loved my work while I subbed for her for nearly a full month, and they eventually fired her and made me her replacement after another interview. It was definitely unusual...
It could have potentially put pressure on them versus imaginary competition, haha, though perhaps they desperately needed to hire anyway.