I can get you a signed edition of the Bible right now as long as you don’t care which company printed it or who signs it

Further right of the bell curve than you just to win the silly semantics game you're playing: if you're calling it "The Illiad" and not "Ἰλιάς" you are defacto referring to the book titled "The Illiad" which is the English translation which indeed had a much more recent publication date than the original work.

You say, as you spell 'The Illiad' in English, the earliest instance of which was translated in the 1600s.