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Actually, there are two distinct characteristics of man which - if you believe them to be unique - almost demand that any being which possessed them would inevitably invent the existence of god.
Firstly man is extraordinarily good at recognising patterns. Not just simple patterns - but complex patterns that develop and change over time. Secondly, man (in my view) is probably the only living creature that believes in luck.
If you accept those two arguments it is absolutely inevitable that primitive man would invent god. Why? Because primitive man would rely on, hope for and depend upon good luck to bring favourable weather and bountiful harvests. Man would want to know why some harvests were good and others bad. He would inevitably look for patterns that might be influencing the harvests. Over time, primitive man would start to believe that if he behaved in a certain way, he was more likely to be endowed with good fortune and a good harvest.
From there, it's not a giant leap to think that there must be some "being" who dishes out all this good fortune - and that the duty of man is to please this being. You've already got the raw ingredients for a god. In my view, any primitive creature who believes in luck and who can recognise complex patterns will inevitably invent a god. To a primitive being, there would be no other way of explaining the world.
This also explains why - as man becomes more sophisticated - his belief in the possibility of god gets gradually diminished.
Here is something that I agree 100% with you.