Live "out of" or "in" your car?
I believe it originates from the phrase living out of a suitcase. Supporting this is a Google ngram plot showing the phrase with suitcase preceding car by almost 30 years.
Lexico defines live out of a suitcase as
Live or stay somewhere on a temporary basis and with only a limited selection of one's belongings, typically because one's occupation requires a great deal of traveling.
Living out of a car is typically done because one lacks a traditional residence, but the idea is similar in that all of one's belongings are in the car.