Is the aforementioned selling method permissible, given that the seller does not own the garment but rather displays one sample and asks the customer to pay the full amount upfront, after which the product is manufactured and shipped to the customer by the printing company?

This transaction is permissible. It is a supply contract for a manufactured good, and it falls under the rulings of Istisna'a (manufacturing contract). Payment can be made in full or in installments. A resolution was issued by the International Islamic Fiqh Academy stating that if a supply contract is for a good that requires manufacturing, it is Istisna'a. If it is for a good that does not require manufacturing and is described with certainty (mawsufah fi al-dhimma), it is permissible if the full price is paid in advance (salam), otherwise it is not permissible because it is a binding promise that resembles selling a deferred payment for a deferred payment (bay' al-kali' bi al-kali')—unless the promise is non-binding. There are two other permissible methods: an agency contract with a fee (wakala bi ajra) and a murabaha contract with a promise to purchase.