The Bible describes the Patriarchs as journeying to Mesopotamia and getting their wives from there. In the case of Isaac and Jacob, a command is given from their fathers not to take a wife from the daughters of Canaan. Since the Bible could not have been composed in its written form before c. 722 BC, when the first evidence for mass literacy and a large population appears in Judah, and since First Temple Judah was antagonistic to Assyrian and Chaldean rule, it makes the most sense to place the composition of these narratives either during the Persian or Exilic periods. The Hellenistic Period is unlikely, since the geography expressed in Genesis contains no evidence of Hellenistic influence.
The Babylonian period would make little sense for the composition of the Patriarchal narratives. The command to take a wife from Mesopotamia would be nonsensical to any Jew living in the vicinity of Babylon. The frequent references to northern, instead of southern Mesopotamia in the Patriarchal narratives would also be odd if those narratives were written in the Exilic era. The placing of the completion of the writing of Genesis in the Early Persian period would also make sense of Genesis 11, allowing for a possible Jewish settlement in Northern Mesopotamia. In short, it is most likely that the Northern Mesopotamia of Genesis reflects conditions of the Early Achaeminid period of the First Return, or, possibly, a later return.