I recently moved to Ireland (an EU country).
When I wanted to get set up with a new GP, I was offered an appointment the same week. I wasn't ready to actually go in yet, so I asked for one the following week. My wife needed some specialty care, and when we made the appointment they were very apologetic that they could't give us an appointment until 2.5 weeks later. (For a non-emergency consult, preparatory to a specialty surgery.)
Meanwhile, in the US, when we tried to make GP appointments, they were routinely not available until 6-8 weeks later. And that's if it was even possible; we had 2 GPs just leave the area over the course of a few years, and in both cases we were left to find our own replacements, despite the fact that both were part of larger medical practices with at least a half-dozen GPs each (plus others).