They cull resumes in the pile by degree - you can get in with a reference nowadays but most places the front door is closed unless you have a pedigree.
Maybe things are different now, but I'm on my third year with my current employer, and I found them organically, sending my resume out on Indeed. Admittedly the MS stuff was largely kicked off by contacts, but that's the only instance throughout my career. And those connections were gained through other work, of course.