Nobody knows what religion means, so this is not one question, but a collection of them. I would claim that for three prominent meanings the answers are not consistent.
Literally, from its etymology and earliest usage, religion is simply 'the link back' -- whatever binds you to an earlier history. Everyone has that, and brings it with them. That would give the answer 'no', whatever you come forward from, you are bound back to it.
In one modern sense, religion is about relationships to the supernatural. But that requires a later notion of the natural to be interposed after the tradition has lost its claim to accurately explain nature. Until it becomes obvious that people are maintaining it out of context, what we now think of as a religion is just immature science (including rational psychology as a science).
Only once the choice is made to maintain its truth whether or not it really fits to the context, because it supports meaning and a given psychology, can there be a notion of anything supernatural -- up until that point, there was just nature, and the system explained that nature. It assumed we knew on its basis how people worked, naturally, and what was ultimately best for them.
So although they had intricate ritual habits and strong theories of how the universe worked, from one POV, Homer preserves evidence that at some point Greeks seem to have had no criterion to separate religion from simple knowledge. So your answer is 'yes', primitive cultures that arise without an already separately identified science should logically all naturally lack the concept of religion in this sense.
In another modern sense, the sense in which Confucianism is one, a religion is a collected set of principles whose effects are enforced by an institution. That approach gives the opposite answer for exactly the same reason. A government is an institution, and any set of principles either is religious, or will be soon enough, because the world changes, and we choose for certain things not to change with it.