To clarify, I mean the gods are not real in the sense of literal omniscient, all powerful beings who take human form. I would argue that anything is as real as people believe it to be, so in that sense, I suppose gods are as real as any character or audience member makes them.

I say the symbolic odyssey in this movie is Odysseus learning that humans, not gods, have the ultimate power and ultimate responsibility to create and uphold a moral order. That's why he leaves at the end. He chooses to do the right thing, own his violation of Zeus's Law, and honor his dead men, even as the rest of the world is choosing otherwise.

Okay, so why can't you tell this story in a world with gods?

First, agency. As soon as you introduce gods into a story, characters lose agency. If the gods are overtly present and giving orders and making people fulfill fate, Odysseus is largely absolved of the Trojan Horse and Troy. This is an interpretation that, like Oppenheimer, shows how one man's choice, a choice that seems like the best in the moment, leads the ruin of civilization and humanity.

Second, the Athena character has to be human first and foremost. I'm not convinced that the story has meaning if this Athena isn't just a girl that they killed in Troy and the memory of her.

The original Odyssey is about what happens when someone disrespects the gods. This one is about what happens when someone disrespects humanity, society, people, customs... if they 'kill' a god, the story isn't about people anymore. If a god chooses the form of a dead woman, Odysseus isn't really learning anything and the story becomes about the god, not the human. (I'm somewhat open to the 'Odysseus sees Athena as the woman because of his own mind' theory... somewhat.)

Here's some evidence in support of 'the gods aren't real in this film' theory.

The epigraph "In a time of supposed magic" primes us with doubt. 'Supposed' is a choice, and I think it is meant to make us skeptical.

Mentor. In the original text, Athena takes the form of Mentor. Telemachus alludes to this with the 'you have wise eyes' comment, and it makes you think a reveal is coming later. But it never does. In fact, it's the opposite because Mentor is killed in the temple. He's just a human who is given god-like status by the perception of others (including, and this is important, the audience).

The symbolism of a group of people invading a sacred space and killing the would-be human form of Athena in that temple is perhaps the most 'humans are in control, the gods are just an idea' thing that I've ever seen. It verges on too heavy handed.

The 'wise eyes' comment comes back. Telemachus says this to his dad who is not a god. This is to the point that being godlike is about how others see you or to the point that there is some divinity in everyone.

Zeus's Law. AKA Xenia. This is the idea that anyone could be a god and should therefore be treated with hospitality, and if we take it a step further, I again say this means that everyone is a god, or contains divinity in them. (This relates to some fascinating religious theories. I'd start with Baruch Spinoza.)

'Why isn't Hermes here?' I see this a lot, since Hermes is a key player in the original epic. For me, the answer is because he doesn't exist.

Chance and coincidence. A major recurring plot point is the lots boys drew. Everytime it shows up you have to think about chance and how humans manipulate chance. There is also Odysseus's comment, to paraphrase badly, that 'after the cyclops the men saw bad weather as Poseidon cursing us.'

The whole conversation between Athena and Odysseus about signs and symbols violates the very rules they are discussing. She is saying the gods don't have a direct chat with humans, they give signs, and she says this while having a chat with him. It's incongruous, and I argue intentionally so.

Athena's affect. Admittedly, this could be a character choice, but Athena in the film is very calm, stoic, almost muted. She comes across as so achingly human, especially in later scenes.

tl;dr I think the Athena character is only a goddess to the extent that Odysseus (or the audience) believe her to be a god, but ultimately she exists only in Odysseus's mind as a manifestation of his guilt and his own way to rationalize the world. I think the story Nolan wants to tell is more powerful if Odysseus is haunted by the memory of a nameless murdered girl instead of guided by an all powerful goddess.