What date did the ancient hebrew civilization begin?

No one knows. The monotheistic Hebrews date back to approximately 2000 BCE, but the Hebrews are far older than that, possibly being an identifiable group for more than 10,000 years.

Answer:

The Torah places the Flood in 2104 BCE. The earliest Hebrews, descended from Shem (Genesis ch.11), lived in Northern Mesopotamia in the centuries following the Flood. Before that there were no Hebrews.