Can the sale of cars by banks in installments be analogized to a forward sale (بيع السلم) rather than to the sale of something one does not own (بيع ما لا يملك)? And what is the reason for not considering the full upfront payment of the price an impediment to that?

The bank's sale of a car before owning it cannot be justified by Bay' al-Salam (forward sale), because Bay' al-Salam involves a described item that is a liability, with the full price paid at the contract session. In contrast, the bank sells a specific item it does not yet own. This falls under selling what one does not possess and profiting from what one does not guarantee. Although installment sales are permissible, it is prohibited to sign the sale contract before the bank takes possession of the commodity. It is permissible for the bank to take a seriousness guarantee from the prospective buyer in the case of a promise to purchase, such as a performance bond from the original seller, especially if the customer suggests a specific seller.