Is it permissible to purchase goods from China for customers with payment upon receipt and inspection, and is this considered selling what one does not own, or a promise to buy?

There is no harm in that, as long as the customers do not bear any responsibility, are not obligated to take the goods, and the seller has acquired ownership of the goods and bears the responsibility and consequences of the purchase. The matter is merely an offer and acceptance or a promise, and the sale is concluded when the customer receives the goods and is satisfied with them. This is not related to selling what one does not own, nor is it a salam (forward) sale, which requires immediate payment of the price at the time of contract, because the customer does not buy the goods until they arrive and are received.