While not a direct answer to your question, I've written about the almost universal nature of ancient slavery here. I've also touched on ancient slavery in a couple of other questions if you want to find them on my profile page. Legal slavery was treated as the default in most pre-modern societies, and certainly all urbanized, literate, Old World cultures.

While not ancient in the same sense, the Inca can be taken as an example of a major centralized culture without slavery in this answer from u/Qhapaqocha, though as one person points out, even that can be challenged.