Are Homer's Iliad and Odyssey the oldest versions of those stories we have?

The Iliad and the Odyssey cover two episodes of the Trojan War - the wrath of Achilles and the homecoming of Odysseus respectively. As far as I know, it's generally held that these two epic poems were based on older traditions - Homer (assuming a single person created both, which I know is far from consensus) did not make these stories up himself.

Do we have any access to older versions of these stories (through any means, including material culture)? If not the stories themselves, then characters and/or episodes that are included within? Do we have any information, for example, about Achilles and Odysseus from before the poems are generally dated?

I know that there were real life Trojan Wars that might have served as inspiration, and there are parallels in stories in other cultures.