Who was first titled "the Jew"?

I hear a lot about who was “the first Jew” and who can’t be. Adam and Eve – not Jewish, first humans but not first Jews. Abraham – many insist he is the first Jew, but he is titled “Abraham the Hebrew” and not “Abraham the Jew”, as the term “Yehudi” (Jewish) didn’t exist yet during his time. The term “Judaism” only became a thing after the sons of Jacob got their land and the subsequent wars (based on Jacobs son Yehuda).

I remember one of my teachers once said that the first person named as “Jew” in Jewish history is Mordecai the Jew (מרדכי היהודי), but i am curious to know if anyone has any more insight on this (relevant?) piece of history.

So who is the first person titled as being Jewish? What are your opinions, disagreements, enlightenments, on this question?