If you had an actual problem that needed a specialist, and you had a PPO plan (most people do), you'd pick a regional provider chain and find their urgent care, walk in, and get an initial consultation done the same day. Stipulating you need a specialist, they'd make a referral, which you could either use directly or use to book with another specialist. Last time, I was 6 weeks out for my referred specialist from my PCP, and 3 days out from the one I called.

It is annoying to book an annual physical, and to establish a long term PCP relationship. It takes forever to book my PCP; months. But I've learned simply never to go to my PCP directly for stuff.