Why was Abraham known as the Father of Judaism?

Answer 1

This is based on several verses taken as a whole. Abraham is promised by God that he will become a great nation (Genesis 12:2); and it later states that Abraham's son Ishmael, born of Hagar (Genesis 16:15) will be a numerous people (Genesis 17:20); while Isaac, born of Sarah (Genesis 21:3) will be Abraham's choicest seed (Genesis 21:12) and the bearer of God's covenant (Genesis 17:21). Isaac had two sons, Esau and Jacob (Genesis 25:21-25). Esau willingly sold his birthright to Jacob (Genesis 25:30-33), entitling Jacob to get Isaac's chief blessing, which he did (Genesis ch.27). God is never described as speaking to Esau, who plotted murder (Genesis 27:41); but He spoke to Jacob repeatedly; and in one of the prophecies, He gave Jacob the title of Israel (Genesis 35:10), which is the title of the Jewish people, Jacob's descendants.

Another Answer:

Abraham, Isaac, and Jacob (Israel) were never called Jews but rather Hebrews:

Genesis 14:13New King James Version (NKJV)

13 Then one who had escaped came and told Abram the Hebrew,

The term 'Jew' is predominantly the tribe of Judah, the fourth son of Israel (there are 11 other tribes though Benjamin was mostly absorbed by Judah when the Kingdom split - some of Simeon and Levi as well are in this group as may be the others over the generations).

A rule of thumb: all Jews are Hebrews but not all Hebrews are Jews.

Of Israel's 12 sons: all Jews are Israelites but not all Israelites are Jews

Answer 2

Abraham was known as "the father of many", but the Jews see him as the first Jew because he was the first of the Hebrews to recognize the existence of one God above all others.

Muslims see him as the first Muslim for the same reason.

Answer 3

Jewish Tradition holds that Abraham was born around 2000 BCE. No exact year is known.

There is no archealogical evidence for Abraham's existence, so this is purely a belief/tradition.