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.
Possibly, Samaritanism is closer to the religion of the ancient Israelites than contemporary Rabbinic (or even Karaite) Judaism is.