Is it permissible to sell products that the seller does not fully possess at the time of عرض [display/offer], then buys them after the customer orders them, pays their price before delivering them to the customer and receiving the money from him? And is this considered selling what one does not own?

If the sales contract is not concluded until after the commodity has been purchased and possessed, then it is valid and does not fall under the category of "selling what you do not possess." The prohibited act is selling the commodity before possessing it, by concluding the sale with the buyer and then purchasing the commodity. This type of sale is forbidden and void.