Alright I'll try this again with a hopefully more fleshed out answer. The academic world is conflicted on this. Prior to Schliemann and Sir Arthur, it wasn't even certain that the cities mentioned by Homer (Mycenae, Sparta, Troy, Knossos, etc.) existed historically. Schliemann is now rather controversial, in part because of [his unwavering belief in a Homeric Troy, and an epic Greek Bronze Age.] (https://sites.psu.edu/heinrichschliemann/controversial-questions-arise/) While it is now generally accepted that Schliemann's site at Hisarlik includes the Homeric Troy, prior to him, Troy wasn't thought of as a true historical place. So that gives you an idea of the historicity of Homer--it's only in the last 150 years that the Iliad and Odyssey have been seriously considered historical and able-to-be-proven. Of the primary Greek heroes in Homer's works, Odysseus is probably the hardest to find archaeological evidence of, simply because he was (assuming he was a historical figure) the king of a small rural island, as opposed to a large [administrative system such as Mycenae] (https://ancient-world-project.nes.lsa.umich.edu/tltc/wp-content/uploads/2016/05/BA_Shelmerdine_2008_Cambridge-Companion-to-the-Aegean-Bronze-Age_Economy-and-Administration-pp.-289-309-split.pdf) (although some folks think that the cities of the Argolid plain were in fact entirely independent entities).

In fact, there has recently been a debate over whether or not the modern island of Ithaka is even the Ithaka that Homer mentions, or if it was settled and named after Homer's Ithaka later on. The Smithsonian provides a nice summary of that theory. However, a Bronze Age administrative center ("palace") has been discovered on the modern island of Ithaka, that could perhaps be Odysseus's palace.

To further complicate things, "Homer"'s poetry was recited orally from memory, and it is almost certain that "Homer," if he existed, was not the sole author of the Iliad and Odyssey. So it's kind of like fanfiction or a roleplay based on already-extant myths--it can tell us a lot about the values of people in the 8th-ish century B.C.E., it is not exactly a solid primary source account of the events of the Iliad/Odyssey. One scholar says: "it has to be acknowledged that Homer was never in fact a stable entity from which a sure base of culture and learning could flow. (In Greek homerizein, ‘to Homerize’, after all can mean ‘to lie’," (pg 325).

If you have access to JSTOR via your school, here is an article that analyzes the patterns of oral poetry and uses them to discuss the historicity of Homer, and here is a really good article that looks at the Albanian tradition of oral poetry, which includes a Homer-like figure, in order to better understand the concept of Homer. It's a really great introduction to some of the big ideas in oral poetry, if that is something you're interested in.

With regards to Odysseus himself, there is evidence of Odysseus-age habitation of the Ionian islands, both the modern Ithaka and the possible-historic-Ithaka on Kefalonia. But unfortunately, much like the other mythical Greek characters, we cannot prove that they existed. It is possible that Odysseus is an archetype or a combination of a few historical figures (this is what I personally tend to believe). Some people are saying that they've pinned down the date of Odysseus's return based on a solar eclipse and Homer's description of the return, which you can read about here.

Personally, I want Odysseus and his buddies to be real historical figures, but they sort of exist in a quasi-historical limbo, where it cannot be proven if they were "real" or not. Of course, these myths are "real" in the sense that they've had an influence on society, but that's not what you were asking.