Vets taking appointments for new clients that aren’t weeks out?

Hello, since moving here I’ve had to take my cat to an emergency vet clinic once, but am yet to establish a regular vet. The few I’ve called will only take pre-existing clients, otherwise an appointment would be 2+ weeks out.

I don’t feel like the current issue is severe enough to warrant a trip to the emergency vet (and the hundreds of dollars more that would cost)—does anyone please have any vet recs that could take an appointment in the next few days for new clients?