When is the first doctor's appointment?

So I recently moved to a different state (in the US), and it will be about a month or more before my insurance will switch to one that is widely accepted in my area. There are some doctors here that will accept my current insurance, but they are few and far between and it will be much more expensive. I'd rather not see a different doctor the first appointment than who I will see for the rest of my pregnancy, and I hate to pay so much more than I might have to. So IF I am pregnant this month (my first month so unlikely), I will be about 4 weeks on August 11. When would I need to make the first doctor's appointment?