Recruiter reached out while I was also actively searching (and I had been for a while) and I ended up liking the position and the team. I don't know what "using my network" would even mean - just limit myself to a handful of companies (that I know nothing about) and cold-message people that I haven't spoked to in months/years so they can maybe check if there are open positions (which I could have looked up on the com…
One example: look at the people on your direct team from your last job, and see are any of them working at companies that might interest you. If they are, message then directly and ask if they've got an opening in your area coming up.
You don't need to be lunch buddies with the person. There's plenty of people I've worked with over the years that if they reached out saying they were looking j would have no hesitation referring internally, and at even a medium size company a job opening can appear.