Time-sensitive CPAM (or PUMA?) application for American holder of passeporte talente (renown) without salary

Thank you for this forum. I've spent many hours online and still can't piece together what to do. An American citizen, I arrived in late August 2023 with a VLS-TS. I networked in Paris for a year concerning potential work, then successfully applied for a passeport talent / renommée internationale (4 years), which arrived remarkably quickly (12 days from application... it was like the Prefecture was running in the Olympics!). I have some upcoming contracts but no salary nor a registered entreprise -- so I believe I would need to go through PUMA, is that correct? And pay URSSAF?

Foolishly, I didn't apply for CPAM, PUMA, or a social security number in my first year, though I did need to see two doctors. I paid out of pocket (my expat insurance didn't cover it). I now may need to have surgery here in January 2025. I have all the documents to support a CPAM or PUMA application (though my original California birth certificate from the 1960s is small -- I don't know if it needs an apostille or...?).

Is there any way to expedite the application? I go to pick up my carte de sejour/talent from the Prefecture in mid-October. I would really like to not have to buy additional expat insurance (which expired a week ago), and I need to get the application in and recorded soon so I can return to one of the doctors and then get scheduled for a surgery.

Last Q: since I hadn't already registered, I can't seek reimbursement from the feuilles de soin I already have, is that right? Merci!!!