Overall, the simplest way to understand how we, and monkeys, who had a common ancestor to us, would develop "theism"....would be to take what we already know about pattern recognition in animals, and allow it to follow its due course.
Studies show that primates are great at pattern recognition.
We all have a propensity to scan for patterns that represent potential resources or danger for example.
If you hear a noise in the bush, you are LIKELY to try to associate it with potential sources, a bear, a lion or a deer, etc.
If mostly worried about being eaten, the first thought is that it might be a threat.
This is an abstract concept, as you don't see a threat, and you are interpreting a snapped branch as having been snapped by something dangerous.
If we were to then hope we don't get eaten, and, we don't, we store that event as "There was a bear, and, I hoped it didn't eat me, and, it DIDN'T!
If positive, say, looking for food, we might hope we find it, and, then we DO!
If this works even once or twice, most animals that have pattern recognition will repeat "whatever worked before"...hoping it will work again.
For birds, this might be a series of twitches or aerobatic maneuvers or calls, that are repeated...or just going back to an empty bird feeder over and over again because it had food before, etc...same concept.
The placing of rocks in the crooks of trees before battle with other monkeys, etc, falls into this sort of behavior....if "it worked" before, it will get repeated.
Baseball fans who wear lucky socks, hats, jerseys, etc...are simply following their instincts to repeat behaviors "that worked before".
Primates can work together, share tools, loan a tool, and have it returned when done...and can make strategies for raiding food or battling other groups of monkeys, etc.
Plans can include one group acting as a diversion to distract the other rival gang...another abstract concept, so the main force can storm a position, steal food, etc.
How was that plan communicated without words?
Essentially, they look at each other, make expressions, gesticulate, use body language, and, yes, make different sounds.
Think about a Navy Seal Team, they can make a few gestures, and the team knows who is to do what, and when and how....same principle.
They can pass knowledge down to later generations, so their descendants can winnow wheat, use a stone as an anvil to make the hammer stone more effective, grind a stone flatter to have more contact area, and so forth.
So, sure, we had common ancestors, but most of what makes us look as we do now vs our common ancestor, happened fairly recently in geological time at least.
So, it seems to be common for animals to act as though there is a higher power...whether they think that or not (Don't know what they are thinking of course).
If we see a human do something, we interpret it in light of what we know about humans.
50 years ago, a human walking along talking with no one nearby was deemed to be crazy...or praying, etc.
Now, they are deemed to be crazy, praying, or using a cell phone earpiece, etc.
If we see humans stack rocks in patterns, but for no known purpose, we consider if it might be religious in meaning, such as Stone Henge.
If we see monkeys stack rocks in patterns for no known purpose, we also consider if it might be religious in meaning.
religion, for a monkey of course, can simply be that extrapolation of "this seemed to work before"...a version of doing something that brings luck, etc.
They don't need to have a vision of a higher power per se...just the concept that something seemed to work before, so its repeated....analogous to any ritual, lucky hat, etc.
Ask a fan who wears a lucky whatever or who has rituals before or during a game that he thinks influence the outcome, WHY he thinks that a hat on a guy in front of a TV, can change the outcome of a game a thousand miles away...
...and if honest, they will essentially just feel like it worked before, so it must be lucky.
That's theism in a nut shell....and everything after that is about logistics and organization, etc.
The fan will not truly understand WHY he thinks something is lucky..as in what forces enact the desired changes/outcome?
The fan, and the Chimp, are essentially at the same level of understanding at that point....there is something that you can appeal to, that can influence what happens....and that's as far as it goes.
Primate religion, watching a game on TV.
what do you think about the idea that other species may believe in some sort of higher power?
Still doesn't make it true. Religious people have been arguing for a while now that religiosity and belief in a higher power is somehow hard coded into us, the fact that maybe chimps have a similar belief says that maybe it is hard coded into us... but that isn't evidence of it's truth, only evidence that at one point it was evolutionarily beneficial to our ancestors. I've even heard atheists talking about how religiosity can benefit a social species.
EDIT: Curse you necro-thread! Tricked into replying again!
We are hard wired to recognize faces, even in a pug's ass, toast, etc....it doesn't mean a pug's ass has a face, despite its face looking like an ass, etc.
Hmmm, on a pug, its face DOES look like an ass, and, people have seen god's face in a pug's ass.
That means if you look at the dog backwards, you see god.