I reckon you will be very hard pushed to find information on when any mythology started, and where, especially Greek. Mythologies are not like histories in this regard. No one really sits down and writes them as such, or at least history cannot show this to us, mainly owing to their ancient, ancient nature (and by 'ancient' I don't just mean relating to time).
They creep out of a people's collective imagination in a seemingly natural form, because humans need analogies in order to understand the workings of their minds and hearts, and the unknown forces of the universe around them. That's what the gods and goddesses represent. They bring into focus for the human mind such things as 'hate', 'deceipt', 'carnal instinct', 'love' and 'revenge', plus things like 'the sun's passage through the sky', 'the passing of time' and 'the progression of the seasons', 'the destructive forces of nature', 'fertility' and so on; all of which are pretty grand and unwieldy ideas, phenomena and entities, especially for the ancients not 'blessed' with scientific reason that allows these to be demystified. Gods and goddesses provided (and still provide) a graspable personification of these and much else besides.
It is typically the shamanic, priestly and spiritual 'authorities' who refine and combine mythologies that have already emerged for whatever purposes, but I've never come across anyone attempting to detail the origins of mythologies. The closest you may come would be in the work of Joseph Campbell, who was and still is (from beyond the grave) the world's leading comparative mythologist. Perhaps if you were to mention specific myths that you had in mind, it would be possible to shed more light on them.