Did Greeks or other ancient polytheistic societies see their gods as actually existing or more like how we see super heros and comic books?

I'm going to talk about the Greeks specifically as that's the ancient society whose religion I'm most familiar with.

If 'how we see super heros and comic books' can be taken as 'a commonly and overtly acknowledged fiction' then the answer is definitely no, the Greeks did not see their deities like that. But the nature of ancient Greek belief is complicated, and this needs a bit of unpacking.

The nature of ancient Greek literary sources places us in an unusual position; we have access to lots of cogent descriptions and discussions of Greek spirituality, found in philosophical dialogues, poetry, histories and many other places. This provides us with a constellation of individual understandings of the cosmos and the Gods, but the key word here is individual. Merely accounting for vital statistics these perspectives come from different periods, different political and cultural environments within Greece, and with different authorial objectives. As a body they overwhelmingly reflect the property owning, affluent, lettered class of ancient Greek society, a class able to rely on slave labour to allow the time for considering these sorts of things not to mention writing about them. Any one work, from the Iliad through Hesiod's Works and Days through Diodoros Siculus' Library of History, can't be taken to automatically represent common spiritual interpretations or what the majority of Greeks as a whole understood. What this does accurately reflect is the collaborative and consensus based nature of Greek religious belief.

There's also the problem of the nature of ancient Greek 'faith' with regards to spiritual matters. It's fairly common to portray ancient religion as purely transactional, dominated by the notion of bargaining with deities for desired results, and this is not without cause. The intersection of specific rituals and beliefs with political identities also gives a rather utilitarian gloss to the sincerity of belief in ancient Greece. When authors talk about sharing in the Gods or Greek religion as one of the defining aspects of being Greek, or one reads about the specific, often mandatory, local festivals in specific city-states, it can be hard from a modern vantage to not assume a cynical view on the whole thing; people wanted to be active members of a community, those communities had various litmus tests for spiritual activity that had to be passed to make life easier or ease interactions with everyone else, faith in the shared spiritual activities was not an important factor, therefore many people were simply paying lip service to all of these things as a kind of shared social fiction. The problem is that, even with the requirement to demonstrate and possess faith in deities or religious principles, this can be used to describe religious behaviour and social structures in monotheistic societies or those for whom faith is an important stated virtue. This is not a situation which uniquely makes a polytheist more prone to cynicism or understanding spirituality as fiction.

We're also more prone to question the presence of deep conviction or certain knowledge in ancient Greek religion because it was completely displaced by other religious belief systems. Any time we read about Zeus or Achilles or the Titanomachy we know the stinger at the end that the original ancient people didn't; that one day these gods and the spiritual behaviour that went with them would be abandoned, and the world would keep turning. If these beliefs were more than shared superstitions then surely all of those millions of people wouldn't have uprooted their religious heritage in favour of foreign belief systems like Christianity so completely? A useful response is to once again look at the dominant (and surviving) voices from the eras of Christian ascendancy; the powerful of society in a time when increasingly few of them are sympathetic to the cause of the old religion. It's also an era where the state and economic supports for the temples and their priests and their mysteries are being kicked away, taking away the ability to fully participate in traditional activities and much of their trappings. What good is it to follow the ancient Greek gods if you can no longer consult an oracle, take part in the Dionysia with your fellow citizens, or worship at a temple that isn't slowly falling apart? This is not to say that no ancient Greek actually converted to Christianity out of genuine conviction, only that certain decisions become more than just individual ethics when an option becomes less viable.

The solely historical and literary existence of ancient Greek polytheism also grants us an additional remove from a living and immersive society, one in which all facets of daily life were thoroughly integrated into spiritual insights about the universe. For us, these deities and the mythologies going with them are fictional on the same level that a comic might be, for us they are explicitly and entirely fictional. That makes it easier to imagine that they were always seen that way.

My understanding of ancient Greek society is that whilst faith is not an appropriate word their spiritual conviction, or perhaps even better put their spiritual sincerity, was strong, and not lesser than those belonging to belief systems surviving to the present day. As I mentioned before these gods and their doings and the workings of the universe were inseparable from daily existence. Even in the periods where the Gods were generally understood as humanlike in form and personality they remained the embodiment of fundamental forces. Helios did not simply represent the sun, or have the powers of the sun, he was the sun. Aphrodite was not just very desirable and beautiful, she was also referred to in the context of cosmic forces of attraction. This fundamental place of the Gods in how the Hellenic universe was constructed can be seen in some of those individual perspectives I was talking about; even authors with fairly particular views on spirituality and existence, like Plato, would refer to the Gods in this way, as cosmic forces foundational to all existence, even as their personas or natures were debated.

I also don't feel that individual views were more divergent or the profusion of them represents a general lack of sincere belief, simply that a lack of a single Greek dogma made a wider range of opinion difference acceptable than in some other periods and environments. This is also where beliefs as created by consensus comes into play; different communities had different specific rituals, aspects of Gods that they worshipped, even specific local deities. A long running debate in the study of ancient Greek religion is whether or not all the Greek populations actually believed in the same 'Zeus' or 'Athena' with different aspects, or whether the different local interpretations were effectively different gods with enough similarity to be branded under the same general heading. In this context, talking about the actual existence of Gods, I would characterise this as investment in the beliefs that made most sense to particular communities and that had meaning for them. This and the expansion of Greek spiritual interpretation by 'fanfiction', almost, can seem similar to how comic books or other shared continuities can be expanded by new entries, but the key difference is the sincerity of the new interpretations offered. Knowledge that an interpretation innovates or has few precedents does not make advocating it insincere. The Gods were real, and communities of Greeks wanted to give voice and representation to the Gods as they were real to them.

I don't think we'll ever be able to quantify the fundamental question we're talking about here, the nature of religious devotion and its expression too divergent from our own, and with no hard data; we'll never be able to cite how many 'genuine believers' existed in Greek society, or a particular city. We're dealing instead with considered opinions based on likelihoods and the available evidence we have. In the balance, taking Greek society as I understand it from what we have access to, the majority of Greeks across most of their history not only sincerely believed their gods existed but could not imagine a universe without their fundamental presence. What precisely that god represented, what they had done or not done in their existence as a God, what rituals were necessary to interact with them and many other things were up for grabs, when taken across the Greek world as a whole. To borrow my earlier metaphor, the ancient Hellenic body as a whole can perhaps be seen as a galaxy of different religious consensuses. But this was a Hellenic galaxy that shared key understandings, concepts, and a strong belief that they inhabited the same universe. There were Greeks that doubted specific stories about the Gods, with several of our surviving authors expressing doubt or even full blown disapproval of the Homeric portrayal of the Gods. But the latter comes from a place of 'genuine' understanding of the Gods, necessitating sincere belief in their existence and a strong desire to correct or challenge the assertions of others about their nature, and doubting the abduction of Europa's reality does not mean doubting the reality of all knowing, all seeing Zeus, King of the Gods. Whilst for some individual Greeks the commonplace understanding of the Gods, whether across the Hellenic world or in their own community, might have been considered fictional, or the trappings of religion lacking in real truth, I don't know of anything to suggest this was more than the belief of specific individuals.