According to Evolutionary Psychology the sort of development you're talking about is extremely unlikely due to the difference in survival outcomes due to Type I and Type II errors, especially with regard to agent detection.
The classic example is the lion in the grass. If you're a primitive pre-sentient animal on the plains of Africa and you see a patch of grass moving you can either react as if there is a dangerous animal in the grass or assume that the grass was moved by the wind or some other non-life threatening cause. The first assumption will lead you to take more care, run, prepare to defend yourself, etc. while the second will not. If it was just the wind then neither option significantly affects your survival probability. If there is a lion stalking you then the first option is much more likely to result in your survival.
In scientific terms a Type I error is a rejection of a true null hypothesis, in this case by accepting that there is a lion in the grass. Type II errors involve acceptance (non-rejection) of a false null hypothesis. Type I errors in survival situations like this are survivable, while Type II errors tend not to be.
So even before a species evolves to true sentience the ancestors of the species are already likely to have developed to rely more on the assumption that everything is trying to eat them than the more rational but less survivable approach.
The result is that early humans are inclined towards seeing agency in the world around them. Since this agent detection is a major survival advantage it becomes embedded deep in the psychological and social structure, and is trained into the children. Everything that happens is more likely to be attributed to some agent, seen or unseen. From there it's a very, very small step to attribute every natural phenomenon to one or more hidden agents - spirits, gods and so on.
Even the idea of a soul/spirit can be derived from the same line of thinking. When a person dies they go from being an agent to a lump of cooling meat. Clearly some change has occurred, and it's not difficult to make the leap that something has left the body, taking the 'agency' with it. From there you can start having all sorts of interesting thoughts about what happens to that spirit, whether it goes into the environment or moves on to some other place. Fear of death is such a major survival advantage that it's unsurprising that an intelligent creature would combine it with departing agency, comforting themselves with the idea that they could live on after death.
And now we've managed to account for about half of religion, and it's an easy stroll from here to the rest of the fundamental religious concepts.
Of course the theory has all sorts of challenges, but it certainly seems to fit the world as we observe it today. Most animals will react to anomalous noises and movement as if it were caused by another creature. Deer will spook at the sound of a falling branch, even insects react to unusual changes in the normal environment. It's the part between animal and human that is slightly questionable, even if it makes sense to us.
In order to not develop overactive agent detection your early humans would have to evolve in a very different environment where survival was tied more to their ability to rationally process their reality rather than spooking at every unexpected event. If there were no successful predators around for a few thousand years then survival would perhaps be tied more towards working out how to best gather food. Unfortunately the reduction in survival pressure would also likely result in a much longer evolution, and it may even stall completely without a suitable survival challenge.