If you don't have your own eCommerce site (brand.com), you can either manually obtain all the product details (Product images, videos, features and specifications) and upload them to your sales distribution channels such as the digital marketplace and social media platform. Once you receive an order from the customer, you will have to manually place the order from the supplier so that they can fulfil the order directly to the customer.
Print on Demand (POD) is a type of dropshipping but you need to involve in the product design stage. You can also choose to create your eCommerce store with the POD platform and connect to your custom domain. However, you may not be able to access the full site data such as customer contact and online behaviour with this approach. You don't need to look into a payment gateway application if you set up a store on the POD platform but you may need to pay for a listing fee or plan subscription in order to enjoy a lower product cost depending on the chosen POD platform. Take a look at the published article from Shopify (2022) on the '10 Best Print on Demand Companies'.