For each of your procedures, you will need your Green Card and your Social Security Number.This number is really important in the USA. You will need it for most of administrative procedures, like open a bank account, get a driver license (in most states), apply for public assistance etc. Actually, it is not only a number that allows you to get medical advantages, like in most health care systems of European countries.
Sorry I disagree with you....
You DON'T need a SSN to open a bank account, get a drivers license, get in school, get free treatment for children under 18 at the health department, or even get health insurance.
A GC is NOT a path to free medicare! For that you have to have a work history and to have paid into the system.
I DO agree that a SSN makes you life easier in the USA, but I was here legally for years without a GC with a visa and had a very high credit score, credit card, drivers license, health insurance, etc...
Don't sell BS to people.