Hi
Welcome to the HP Support Community.
I'm afraid without the setup ink cartridges, you would not be able to setup the printer. Please reach out to the HP Support in your region regarding this issue, they should be able to help you.
Have a great day!
Please click “Accept as Solution” if you feel my post solved your issue, it will help others find the solution.
Click the “Kudos, Thumbs Up" on the bottom right to say “Thanks” for helping!