There might be someone who could speak more to the question of Homer's original audience, but afaik we don't have access to anything from the 8th cent. BC, when we think the poems were written down, and definitely not from the 10th-13th cent. BC, when the poems were likely composed. But I can speak about its reception in other periods, and maybe a little more generally about how "stories" like the Iliad and the Odyssey were understood.

The Greeks raised all kinds of problems about the Homeric poems, and especially its depiction of the gods, since as early as Xenophanes in the 6th century BC. He famously questions why the gods appear to be like people, only much more powerful, saying that if horses could imagine gods, they would look like horses. Plato has Socrates giving less-than-literal interpretations of the myths, and by the Hellenistic period, you have full-blown literary criticism being performed on Homer by scholars in Alexandria. The idea was that, after centuries of criticism by philosophers, elite thinkers had started to claim that the poems are not literally true but veiled narratives that conceal profound truths, not just about historical events, but about theology and the nature of the world. A great book here is Homer the Theologian by Robert Lamberton, and there was a more recent and accessible book on Alexandrian scholarship that I can't seem to think of now, but maybe someone can point you to that.

But more to your point, did the average person believe in the Homeric accounts as histories? A good resource here is Paul Veyne's short book Did the Greeks Believe in their Myths? He goes through a lot of Greek literature, more the historians like Herodotus but also Homer, to ask how people approached the stories they were told and how they judged their truth. The short answer he comes up with is that people generally thought that stories and myths contained a kernel of truth -- after all, no one would just make up something completely out of thin air, and if it is a plausible account at all, then it must express something that's true or else why would anyone believe it? You could think of the myths in our sense of the word narrative. If you watch the news and hear a biased political narrative, you understand that the politician or newscaster is partisan and trying to stir up emotions, but you may still allow that there's a kernel of truth to what they're saying, especially if you side with them. What that kernel is, though, is up for debate.