Is it permissible to purchase from a factory that manufactures the product after payment, knowing that the products will be shipped directly to an Amazon warehouse, which makes it difficult to assess quality and obtain a refund in case of an issue, and is it possible to request a third-party inspection or a single sample to verify quality?

It is permissible to agree with factories to manufacture specific goods with defined characteristics (an istisna' contract), and it is also permissible to sell these goods to customers based on their request (a parallel istisna') on condition that the two contracts are not linked. The price may be paid in advance or deferred, and the factory may ship the goods directly to the customer. It must be ensured that the factory fulfills the conditions to avoid harming the customer or incurring unjustified shipping costs. If the product deviates from the specifications, the buyer has the right to revoke the contract and reclaim the price.