The word “Jew” follows etymologically from the name “Judah”, Abraham’s great-great-grandson. Judah is Jacob’s fourth son and the fourth son of Jacob’s fist and less favored wife Leah. The second king of Biblical Israel is his descendent.
The first king was Saul, a descendent of Judah’s youngest brother Benjamin. But Saul sinned against Yahweh and while Saul was still king, he annointed David of Judah to be King if Israel by his prophet Samuel.
After David’s death, the kingdom of Israel split into two Kingdoms upon the succession of his grandson Rehoboam, the son of David’s son Solomon who built Yahweh’s temple in Jerusalem, though his Temple really resided in Solomon. The northern Kingdom retained the original name, Israel, and the Southern Kingdom was known as Judah. The Jews are judahites in that sense- cultural and ethnic successors of the southern kingdom. Both kingdoms were eventually lost to conqueroring empires.
Abraham was among the first people to practice what we would call the Jewish faith in earnest- monotheistic veneration of Yahweh, who he knew as El Shaddai, “Almighty God”, though not all of Abraham’s offspring are counted among his children according to the promise Yahweh made to him. Through much of the Biblical Narrative, Yahweh is called “The God of Abraham, Isaac, and Jacob.” It is not accurate to say he was the first Jew, since the name comes from his own offspring. It would be more appropriate to refer to him as the first Hebrew and the father of the Jews.