I think other people can explain it better then me, but here is my (extreme) layperson understanding.

The story is from the 12th century BCE Mycenaean Greece. I think most scholars agree some of the people actually existed, and that some of the events did indeed take place. It was then told mouth to mouth for the next 6 centuries, as in the late Bronze age collapse the Greek culture lost their alphabet and couldn’t write it down.

In the 8th century BCE Homer composed the epic from these stories. The Greek culture had just adopted a new alphabet and his poems were written down relatively quickly after it was composed. Having an alphabet to write down the composition gives you a certain freedom when composing, as you don‘t have to compose in a way that every word will be recalled from memory (compare this to e.g. the poetic Eddas which didn’t have this luxury; and also the Prose Edda which did).