Is it permissible to obtain a car loan from banks other than those compliant with Islamic Sharia, in the event that it is not possible to obtain it from Islamic banks, or is it necessary to settle for monthly car rental despite the financial loss?

Material loss does not permit borrowing with usury to buy a car, for usury is not permitted except in cases of dire necessity. A Muslim must fear Allah and seek lawful means, for whoever fears Allah — He will make for him a way out and provide for him from where he does not expect.