Firstly; what is God?
There are many definitions for God that would represent some people's usage. For some, God is the creator, for others, God is the thing that created everything; for others, God is the most powerful being that exists, for others, God is the (most powerful) principle(s) of reality, and for some, God is everything. God could be anything from a consciousness that created the universe, to the universe itself. So, ask yourself, what is God in this context? What kind of God is it that you want your civilization to not have even conceptualized?
I'll answer for the different options I listed:
God as the universe:
Your civilization would have to be really stupid to not realize there is a universe. If you are conscious, then you are aware of stimuli. If you have a shred of meta-cognition, you are aware of your awareness. If you have an ounce of ability for abstraction, you can then refer to all that you experience (and maybe refer also to the mysteries beyond that experience), and assign a name to it; the universe. If your civilization is not capable of doing that, then its hard to imagine how they even became a civilization, let alone how they are going to make for interesting characters.
So, your civilization will likely have the concept of the universe in hand. So, once one has begun referring to all there is, one might be met with a feeling of immensity. Maybe they have also stumbled upon the concept of infinity, and ascribe this to their concept of the universe? Well, then those feelings will only be stronger. If their minds has their species' equivalent of our tendency to anthropomorphize, then they might very well ascribe a kind of character to the universe; a character that could readily be described as God.
The more general tendency of seeing animacy in inanimate elements is likely a mechanism of survival. It's better to be safe than sorry; if that bush rustles, it's better to interpret it as a predator, and thus prepare oneself or run, than it is to reckon that it's just the wind. This mechanism thus leads to all kinds of feelings of animacy in inanimate things. So, if your species does not have this tendency to feel animacy in things, then it is less likely for them to have even survived in the first place.
However, there can be compensatory mechanisms in this case. If their universe is extremely cold and unforgiving, they might come to the conclusion that it definitely isn't God, because they cannot/will not imagine a being so apathetic/cruel enveloping them at all times. It's then better to just think of it as mindless space and matter.
God as the creator/thing that created everything:
This definition of God, and the previous, are not mutually exclusive.
For God to have created everything, there must be a beginning. If your civilization gets it into their head that the universe has existed forever, then there is no time for a creation, and thus, no creator/prime mover. So, if they for some reason believe/know the universe is eternal, this can explain why they do not believe in a creator/prime mover.
Another way, that has a lot more plot impact, but would be kind of fascinating, is if the civilization has no concept of time. Without a concept of time, there is no beginning; no creation; no creator/prime mover. Not sure how this could work, but I found it too interesting a possibility to leave out.
God is the most powerful being:
It's hard to not have a concept of the most powerful being. If you can conceptualize power as a quantity, then you can conceptualize the most powerful being.
Thing is, if you do not believe anyone/anything is particularly powerful, then the most powerful being might not be alone in that role, nor be anything particularly special. Although that being would technically be God given the above definition, there is few that would recognize them as God.
God is the (most powerful) principle(s) of reality:
Some think God is the laws of reality; others think God is particularly the ultimate law(s) of reality. God is gravity; God is 1 + 1 = 2; God is the fact that all things die, etc.
I think such a conception is sufficiently abstract that you do not really need to explain why your civilization did not conceive of it. It is not really natural to think of rules as a being; we rather think of rules as the creations of beings.
See this video of a guy posing, among other things, theological questions to Hadzabe tribe members.