If the bank can't show me the mortgage note for my property can I file a "quiet title action" to establish myself as the owner of the property?
No.
Arguably you are in a catch-22. There is a long line of case law that a debtor in possession of real property cannot quiet title to his property against a mortgagee out of possession without paying the debt, or offering to pay the debt.
I agree with Attorney Michael Stone. No, you can not quiet title. In fact, there is a 1979 California case on point. Good luck.