Technically Abraham, as he was the one, with whom G-d established the Covenant. Although I'm pretty sure there are lengthy disputes in Talmud arguing that it started with Adam and Hava.
I'm counting from when Yahweh declared Israel his people and handed down the Ten Commandments at Mount Sinai (all mythological, of course, though there may be some real inspiration for Exodus, like the mythological Iliad and the real city of Troy).
The problem with asking "when Judaism started", is that the religion of the Mishnah and Talmud is (very likely) so different from the religion of David and Solomon that they are arguably two different religions, even though one is a descendant of the other.
Possibly, Samaritanism is closer to the religion of the ancient Israelites than contemporary Rabbinic (or even Karaite) Judaism is.
I agree with everything you've said, which is why I earlier said that Judaism is arguably younger than the 5th century BC. The real Israelites were likely not even monotheistic during the time of David and Solomon.