Yahweh as a god existed before the Persian and Babylonic times, but at this point he wasn't a monotheïstic god. On the contrary he even is evidenced to have a wife (can't remember the name at the moment) at this time. The religion kept very much changing afterwards still and it isn't untill the late ancient age/early medieval age we get a somewhat consistent religion that is comparable with the current one.
I have a great article on that laying around at college, but I'm at home now so can't look up. But I can some time this week, if you want some more information on the development of Jewish religion and identity. Though that may be off-topic.
Edit: Yahwah's wife apparantly was called Asherah (thank you google).
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