No such "switch" happened. According to the simplest understanding of Jewish history, Judaism started with one man, Avraham, who recognized the creator of the world. He came to this realization himself, independent of anyone else. G-d blessed him that his descendants would be numerous, and they were. Several hundred years later, his descendants stood at Mount Sinai and received the Torah from G-d.
Every Jew today is either a descendant of those people, descended from people who converted somewhere along the way, or are converts themselves. Judaism does not claim to "inherit" from any other religion as I understand Christianity and Islam claim to.