Hello Evergreen. It's good to do impartial investigations of things like this, instead of listening to what certain people try to spoon-feed to us.
I hope you're open to all possibilities, including the possibility that Genesis contains mythology and assertions inconsistent with science that the Bible writers couldn't have known about.
With that in mind, I submit the following answers for your consideration.
If Genesis were literal, then the earth would only be thousands of years old. Scientists doing an impartial study went to Antarctica and did some ice core drilling. Much like rings of trees, you can read layers of ice to determine the age of an ice sheet. This one in Antarctica proved to be 1.5 million years old. So earth would have to be AT LEAST that old. Here's the link for that: http://www.pages-igbp.org/science/initiatives/ipics/data/ipics_oldaa.pdf
The idea that Cain was banished to be a fugitive does not seem consistent with the idea that he would build a city, hardly a place where you would be a vagabond or fugitive (even if the city only had a couple dozen people in it). The story of Cain seems to have shared information with an ancient Egyptian story. Below is the link with the portion of a book called "101 Myths of the Bible: How Ancient Scribes Invented Biblical History" by Gary Greenberg.
Myth 31: Cain built a city east of Eden.
The Myth: And Cain went out from the presence of the LORD, and dwelt in the land of Nod, on the east of Eden. And Cain knew his wife, and she conceived, and bare Enoch; and he builded a city, and called the name of the city Enoch, after the name of his son Enoch. (Gen. 4: 16-18)
The Reality: The four possible sites for the first mythological city are Heliopolis or Thebes in Egypt or Eridu or Bad-tibera in Mesopotamia.
When God discovered that Cain murdered Abel, he declared, “When thou tillest the ground, it shall not henceforth yield unto thee her strength; a fugitive and a vagabond shalt thou be in the earth.” (Gen. 4:12) Yet, almost immediately thereafter Cain built the first city, a sign of permanence inconsistent with being a fugitive and vagabond. That contradiction underscores the confusion of the biblical editors over the identity of Cain.
Initially, Cain stood in for Osiris (oldest son of the heavens and the earth). In Egyptian tradition, Osiris wandered far and wide to teach skills to humanity. He also built the first city at the site of the primeval hill and each Egyptian cult center claimed to be the place where Osiris built the city. In the Mesoptamian tradition, cities were built at the instigation of the gods with humans doing the dirty work. Various texts refer to the five cities built in earliest times: Eridu, Bad-tibera, Larak, Sippur and Shurrupak, all of which date to the early third millennium B.C.
In Hebrew, the name “Cain” means “smith” or “metalworker”. Smiths were artisans and repositories of crafts knowledge. The early Egyptian myths do not talk about metalworkers, but in Mesopotamia, one of the first cities, Bad-tibera, means “fort of the metalworkers” or “wall of the metalworkers”.
Genesis gives few clues about the identity of the city built by Cain. It lies east of Eden in a land called Nod, and Cain named the city after his son. His son’s name was Enoch, but ancient custom treated grandsons as if they were sons and the city could have been named for Irad, Cain’s grandson.
On the one hand, given that Cain the wanderer built only one city, not five as in the Mesopotamian tradition, and that he originally represented Osiris, we should assume that he built the city in Egypt. Since his story originated with the Heliopolitan Creation myth, the most likely choice of city would be Heliopolis, “city of the sun”, east of the Nile where the son rises. Or, given that the first creation story in Genesis derives from the Theban creation account, of which the second Creation story is an offshoot, the first city might be Thebes. The biblical name for Thebes is No, a close approximation to Nod.
On the other hand, as noted in myth #30, biblical editors displaced the story of Cain as Osiris with Sumerian stories about Dumuzi, who according to the Sumerian king list, ruled in Bad-tibera, “fort of the metalworkers”, suggesting that the biblical editors intentionally or mistakenly moved the first city from Egypt to Mesopotamia. The identification of Bad-tibera with metalworking provided a good connection to Cain, the metalworker, at least in the mind of the later biblical editors.
Finally, we have one other city as a plausible candidate. Eridu, one of the first five cities lying southwest of Babylon, always appears first in the list of five, indicating that the Mesopotamians considered it the most prominent and the most important. As the first and most important Mesopotamian city, it makes a good choice as the place where Cain might have built his urban center. Cain’s grandson was named Irad, a close approximation to Eridu, suggesting another possible connection.
In addition, Mesopotamians made Eridu the city of the god Enki. There could be some connection between the names Enki and Enoch, establishing a direct link to Cain’s son. Also some of the ancient literature gives Enki the additional name of Nudimmud, which seems to provide a root connection to the land of Nod, making Eridu the land of Nod.
Any connection between Cain’s city and Mesopotamia, however, would be a late linkage. The city would originally have been located in Egypt.