I have heard apologists say that the oldest manuscript of the Odyssey of Homer is from 2200 years after it was written. I am preparing to teach a class on the reliability of the Bible in which I want to make the point that the biblical manuscripts are more reliable than any other famous ancient document and want to be sure I am accurate.
I really respect your desire to be accurate and to not create a case which will not hold up to scrutiny. My advice is to always tend toward being conservative in the claims we make. That way you will never have to backtrack. It is also the most ethical way to behave when trying to convince people of Christianity. When I hear apologist wanna-bes using canned but unreliable claims, it makes me cringe. Do not do this!
But let me get to your question. The gap can be spun more than one way. Estimates for when the person we know as Homer “wrote” the Odyssey vary widely. (I am putting wrote in quotes because the original was almost certainly oral, not written. Besides, it is debated whether a person we know of as Homer was even an actual person) It is supposed by scholars that the Odyssey was in an oral form from as early as 1200 BC, but that it was written down more like 750 BC. The oldest relatively complete manuscript on traditional writing material, such as vellum, is from about 1000 AD. Therefore the number used by some apologists is not dishonest (2200 years). You can use this number without being deceitful, but you will open yourself to legitimate criticism on two grounds.
First, a relatively recent discovery has been reported of a small passage from the Odyssey on a clay tablet, found in Greece, from about AD 300. This is not a classic “manuscript,” but the quote is long enough that if you ignore this, you will be stretching your case. I suggest you do not do so. Again, it is always better, both ethically and strategically to use a more conservative number.