Buying a car cash and then getting a loan.

A car was purchased in a cash transaction because the seller could only allow me 48 hours to get financing due to their parking situation. I borrowed cash to give to the seller from my mother, but with the intent to secure financing after the fact. My mother offered me a 0% “family loan” with a one year duration.
For the sake of privacy I will use fake numbers to express the financing.

Seller has car listed for $10000
I used $5000 of my savings and my mother lended me $5000.

I want to now secure financing for the car through my credit union to recoup my savings account and pay back my mother. How can I go about this legally? I’m in Oregon, usa. The title was signed by the seller, but not signed for a buyer yet.