I am confused when you use doctor and therapist and discounted fees in related contexts; do you want to see a doctor, a psychiatrist, or do you want to see a therapist for ongoing therapy?

If you call a psychiatrist, who is a doctor that generally sees patients for their prescription drug needs, maybe once a month or once a quarter, they are not going to have discounted fees or like that you do not have insurance/can't pay them.

If you call a therapist, you might get a sliding scale for therapy but "see the doctor first" doesn't fit.

If you want to know if you "should" have therapy, if it would be beneficial to you, etc. I would save up $150, call a psychotherapist and make an appointment, the first one is usually "free" and go talk to them (the $150 is in case it is not free). A therapist's fees usually are personally negotiated, not done by phone/one size fits all. You might not be someone the therapist feels they can work with/help and/or they might not do a sliding fee scale or it might be more than you can do even though it is less than they normally charge, etc. But, talking to someone could educate/help orient you as to what is available and how things work and you could come up with a plan for yourself from there.

There are other options/clinics besides AHCCCS, check out this site, for example Mental Health America of Arizona and maybe ask their advice. It might benefit you to buy insurance, even if it does not "pay" anything to a doctor or therapist, it can often better negotiate for you to lower the fees (because it is in effect a "group" discount since many people are in that insurance plan; it's the difference between Walmart and an independent small retailer where you're the independent :-)