The concept of Judaism and being Jewish only began formally at Mount Sinai. At that point God chose the Jewish Nation over all others to be the Chosen Nation and the criteria for belonging to it were laid down.
Adam and Eve were the originators of Monotheism and anyone could subscribe to their belief system. (Everyone was supposed to believe in it, but starting with Enos, Adam's grandson, people began to move away from God and into the realms of idol worship.) Monotheism did not require a conversion rite; it simply meant that the person would start living according to the tenets that God had brought into the world.
It was only twenty generations later at the time of Abraham that the idea of belonging to a Monotheistic "movement" took root and the nascent beginnings of Judaism could be seen.
Abraham's input into the world was so enormous that God chose him specifically to be the founding father of the Jewish Nation and we take our Jewish identity from Abraham and Sarah.