How do I get my mom's POA started?

Update: I apologize for my earlier answer. I had not yet read that the OP does not have POA when I replied. Lesson learned!

You can go to an online site like NOLO and do it yourself or hire someone from the courts to help you or do it for you . If you do it yourself with NOLO or somewhere like this than it sends with the paperwork instructions of how to get it finalized legally .

If your Mom has Dementia, you are not able to get POA. If she is in the early stages and understands what POA means, you may be able to and if you are able to, have it made immediate. No need for a doctors signature when immediate.

Is the Dr a PCP/ GP? If so, you should have a Neurologist check her out. Ask him for a diagnoses of Denentia and what type. You may need to go to court for guardianship. Lawyer probably will not talk to you or Doctor either because you don't hold POA. Ask the lawyer about guardianship. Its expensive but I think u can use Moms money.

Just for your info, SS does not except POA. So being payee has nothing to do with holding or not holding POA.

I think it is perhaps time to try to use your POA and MPOA (medical) for getting mom's records from the doc. This is going to show the court that mom is not, according to medical records, competent enough to manage her own affairs.

I am surprised by your doctor. The doctor is correct that this is for the court to decide. But guess HOW the courts DO decide? They aren't psychics, so they look at the letters from the doctors.
All that makes me a little concerned that her doc doesn't think that she isn't in control of her own capacity to make executive functions/decisions? Did you discuss this with him/her?

I believe I would change doctors when time is appropriate (likely not in the middle of this). Ask for a referral to a geriatrician, and it won't look like you don't "like" this one, but like you are needing a specialist to guide you.
I would also ask the doctor now to order a neuro-psyc exam so that THAT doctor (who should be very familiar with all this and likely already have a form to fill in for you) can attest to mom's inability.

You can take this up with an elder law attorney. Your current POA will allow you to spend your mother's funds to see an attorney to get everything all nicely and neatly tied with a bow.
I sure hope you will update us on this. It's a bit unusual. Banks ALWAYS say no to POA; it seems their go-to first move. But doctors usually WANT to protect their patients in this way, so this is a bit shocking to be honest, for this old nurse to hear.