There are much older documents from Mesopotamia and Egypt, some of which must have parts that are at least as much of an argument as that. Here is the oldest example I can think of. It's an argument for why the king should send help to a general in the field:
Approximately 2400 BC, quoted in Man and Wound in the Ancient World, p 62
To my lord say this: thus speaks Itur-Asdu, thy servant. There is no physician, no mason. The wall is crumbling, and there is no one to rebuild it. And if a sling-stone wounds a man, there is not a single physician. If it please my lord, may my lord send me a physician and a mason.
There are mathematics tablets and papyri from Egypt and Mesopotamia dating back as far as 3000 BC. Most of them just show mathematical tables or the solutions to problems, but you can probably find an argument or two in there. There are also legal documents and wisdom literature from those places and throughout the Fertile Crescent much older than 600 BC. There have to be examples of arguments in all of that.