Answer:
   
   There are multiple ways to answer this question:
     * Who founded the Jewish religion?
       Abraham. The starting of Judaism is described in Genesis 17, where
       Abram makes a covenant with G-d, and his name is changed to
       Abraham.
       There are many stories told about the founding of Judaism. In one,
       in which Abraham's father, Terah, is a maker of idols, an old man
       walks into the shop to buy an idol. Terah is out, and Abraham is
       minding the store. The old man chose his idol carefully. Abraham
       asked the man how old he was. The man replied, "70". Abraham then
       called him a fool, for worshiping an idol younger than he was. In
       another, similar story, Abraham is minding the store. He smashes
       all the idols but the largest, and puts the hammer in that idol's
       hands. When his father comes home, he is angry, and asks what
       happened. Abraham says that the largest idol got jealous and
       destroyed the others. The father yelled at Abraham because that
       couldn't happen, the idols were just stone!
       For whatever reason, Abraham turned from the moon-worshipping of
       the farmers of Chaldea and came to a monotheistic belief. It was
       at this point that he left his father's house, and started
       Judaism.
       Judaism is the first monotheistic religion. Other monotheistic
       religions, such as Christianity or Islam, were essentially
       offsprings of Judaism.
     * Who was the first to be called "Jew"?
       In the days of Abraham, the term "Jew" was not used. Instead, you
       see the term "Hebrew" ("Israelite" only appears after Jacob
       changed his name to Israel). The term "Jew" didn't arise until
       after the Syro-Ephraimite wars of 735-721 BCE, when the tribe of
       Judah became the dominant tribe. The first "Jewish" reference [as
       a national identity] comes no sooner than with its appearance at
       2nd Kings, 16:6. The Midrash after Rashi establishes the reason
       why "Jew" is accepted throughout when referring, Talmudically, to
       any Abrahamic desendant in the Pentateuch.
       By the way, the term in Hebrew is ivree, which basically means
       "one who passed over", which is a reference to Abraham's origin
       from the "other side" (of the Jordan). In the Torah, you only find
       those terms.
     * When did the Jewish people start?
       The answer would be when the special covenant between the Jewish
       people and G-d started, which required the acceptance of Torah.
       Thus, the answer would be at Mt. Sinai, In the days of Abraham,
       the term "Jew" was not used. Instead, you see the term "Hebrew" or
       "Israelite". The term "Jew" didn't arise until after the
       Syro-Ephraimite wars of 735-721 BCE, when the tribe of Judah
       became the dominant tribe. The first "Jewish" reference [as a
       national identity] comes no sooner than with its appearance at 2nd
       Kings, 16:6. The Midrash after Rashi establishes the reason why
       "Jew" is accepted throughout when referring, Talmudically, to any
       Abrahamic desendant in the Pentateuch.