The Jews (Israelites) of the First Temple era came out of Egypt as slaves, led by Moses.
Heh, that's a very twisted version you're making here.
I follow the Historic version, but even if we follow the biblical one this is still a false assumption.
Judah, son of Jacob, was born in the land of Cnn'aan known today as Israel/Palestine.
Josef, another son of Jacob, has ended up in Egypt after he was trapped and given to slaves owners.
Josef has served there as the Pharaoh's dreams analyzer.
After a while, Jacob and the rest of his sons have immigrated to Egypt.
After 200 years or so, the sons of Jacobs, the Israelite people, were made slaves by the time's Egyptian Pharaoh.
Then comes the Moses story, and the Israelite people are freed from slavery and are making their way to Cnaa'an, where the twelve tribes are each given their own land.
The Judah tribe is being formed in the region of what is today south-western West Bank, including Jerusalem.
The Jews are the citizens of the Judah region, sons of Judah.
You have also made a false equitation between Israelite and Jews.
Jews are Israelite, Israelite are not necessarily Jews.