[TheCoelacanth]

Where are you getting this information?

Everything I can see puts that development well after the poems' composition around 800-700 BCE, though perhaps before they had been fully written down.

If I understand correctly, it's a minority but not completely fringe opinion among historians that a major motivation for inventing the Greek alphabet in the first place may have so that they would be able to write down Homer.

[suddenlybananas]

The digamma was never used in Homer's written form, but the poetic metre in some place is done such that there would be a digamma there and in some places, they don't modify the metre to adapt to the digamma.

[TheCoelacanth]

There's a two-hundred year gap been it bring composed to capturing it in written form. It was in oral form and didn't written down (outside of some short fragements) for the ~200 year.

When the The Odyssey was composed, widespread use of digamma sound was still a big thing.

I can easily believe that anachronistic language was added in the process of writing them down, but the original audience wasn't people reading in a book; it was people who were listening to a poem that had never been written down.

There is a huge amount of anacronistic content, but when it was first performed, language was relatively contemporary at the start.