You don’t need to have a trademark in order to be able to create new listings in the Amazon’s catalogue.

When creating new listings on Amazon, you need to provide a valid product identifier such as EAN, UPC, JAN or ISBN code, unless you were granted an exemption.

If the product doesn’t have a barcode, you will either need to purchase one from GS1 or request an exemption for the particular category.

You can learn more using this “Create a listing” Amazon help page:

https://sellercentral.amazon.co.uk/gp/help/help.html/?itemID=G39EFY66ZLSJQ7PM&ref_=ag_G39EFY66ZLSJQ7PM_h_r0_cont_sgsearch

or “How to list products that do not have a GTIN (UPC, EAN, JAN or ISBN)”:

https://sellercentral.amazon.co.uk/gp/help/help.html/?itemID=G200426310&ref_=ag_G200426310_h_r0_cont_sgsearch

and:

“ASIN creation policy”:

https://sellercentral.amazon.co.uk/gp/help/help.html/?itemID=G201844590&ref_=ag_G201844590_h_r0_cont_sgsearch