Abraham was the first Jew in that he was the first individual to separate himself from the rest of idolatrous humanity and recognized God. That’s why the Torah refers to him as “Ivri”, which means “on the other side”.
It was through Abraham that God re-introduced the teachings of Judaism originally taught to Adam and which were preserved until then by only a few. Judaism was thus transmitted through his progeny, the Hebrews – derived from their being the descendants of Abraham the “Ivri”; or Israelites – the descendants of Jacob/Israel.
However, formally speaking, they only became a Jewish People at Sinai where, en masse, the Israelites underwent a proper “conversion” involving acceptance of God, the Torah, circumcision for males and immersion in the mikveh for all.
While Abraham lived around 1900 BCE, the events at Sinai took place around 1300 BCE.