> If we were to find an inscription of Odysseus confirming he was king of Ithaca during a particular era,

Speculating what would be required to prove various claims or statements is interesting. To prove a claim, it is typically necessary to provide evidence that supports it and to show that this evidence is strong enough to justify accepting the claim as accurate. This inscription would show that he probably existed and was king of Ithaca during a particular era.

> that still is not proof that the Trojan Horse idea came to him from the goddess Athena.

But I do not see the significance here of this comment, no one is claiming a supernatural claim. But of course, ultimately, the level of evidence and argumentation required to prove a claim will depend on the complexity and significance of the claim itself, as well as the standards of evidence that are accepted within the relevant field of study or domain of inquiry.