We can't really answer the question until we know what a god is. And for religious reasons, people are often uncomfortable examining just what a god is. It turns out that the concept itself, while old, hasn't always been the same.
With what we have to extrapolate from, gods weren't always "gods". Humans in cultures that are unlike the PIE-descendant cultures we're familiar with sometimes have concepts that are much more similar to the original version.
In those versions, the world is full of what you or I would call "spirits". Spirits are formless, they have no bodies. This isn't necessarily invisible, but it's definitely not solid either. Spirits also have location, they have no omnipresence. They have personality, and they have names. They can have individuality but it's not always required. The "antelope" spirit isn't just one (there are many antelope after all), but neither would you know the names of each of them nor would it matter. And unlike ghosts, they weren't ever necessarily alive in the same sense that you or I are alive. Many spirits could be friendly, others could be grumpy or downright hostile. You could ask favors of them, or cause them to become your enemy. They didn't create anything in the absolute sense either... some spirits could create this or that, in the same ways that a particular human might create this or that. But none were credited for creating the entire universe, for creating everything. They could be wise or foolish. They might know something that a human wouldn't or couldn't know, but there was no omniscience either. They might wield magic, or might even be able to do powerful things inherently, but there was no omnipotence. Clever or heroic humans might very well best them.
At some point in prehistory, things changed. At least in some parts of the world. Some cultures adopted particular spirits as their patrons. They believed that these spirits interceded on their behalf, at least when they were appeased. That their patron spirits might be more powerful than a competing tribe's patron spirits. Arms races ensued, of a sort. Many mechanisms, but the obvious ones are through more extreme appeasement... this becomes worship. Another is aggrandizement. "My god is more powerful than your god!" That is the seed which will eventually become omnipotence and the myth of "creating everything" in monotheism. We're probably not finished at this point, but we're well into the place where spirits are starting to turn into gods. And while their characteristics will still change a bit, they tend to (even today) retain many of the early characteristics too. They are still formless, though perhaps only when it suits them. They still have presence and location. Heck, they not only have location, but they're still bound to it. If your tribe migrates 1000 miles away, their god probably hasn't come with them and they'll need to worship a new one. Omnipresence will only come later, with the last few final aggrandizements, with monotheism.
So, what you really need is a difference concept of what a god/goddess is. And you don't have to invent a new one, you can just borrow back from the earlier concept. This is also borrowing from the time period where there is less difference between "human" and anything else. If your monotheist deity isn't the only god, and if he didn't create people "in his image", there's just that much less difference between humans and everything else. If you go on your hunt and request from the antelope spirits to be successful, you're sort of talking to them as if they're people anyway. A person who did that wouldn't blink at the notion that the son or daughter of a spirit might not be distinguished from the son or daughter of another person. But they wouldn't be surprised either if they were heroic or clever or long-lived or could even take on characteristics of a spirit again in ways that people couldn't.
If you told them a story about the offspring of a spirit and a human, they wouldn't scoff at that child being normal, nor would they scoff at it being unusual. And I believe that there is enough popularity in these older ideas even today that you don't have to change the story for us either. If it feels as if this isn't good enough, you may be trying to hard to "science-fiction" yours.