You know very well that if we found some shard that said "Abraham" on it, people would ask, "How do you know it's
your Abraham?" And that would be a proper question. And if we found some artifact that mentioned "Abraham, Isaac, and Jacob," they would ask, "How do you know it's
your Abraham, Isaac, and Jacob?"
You may think the latter one is silly and far-fetched, but yet an ossuary from the 1st century was found mentioning James, the son of Joseph, the brother of Jesus, and yet people say, "How do you know it's
your James, Joseph, and Jesus? It think there's no winning this game unless there are multiple, undeniable references that match what the Bible says. Scientifically speaking, it's demanding almost the impossible. You must realize that the further we go back in time, the fewer artifacts we have (especially specific ones [names, places, and events]). And especially since Abraham was not a ruler of an empire or lived in a city, the odds of finding 1 artifact, let alone numerous, are close to zero even if he
did exist. Add to that that Abraham was a Bedouin, not a king (as the records we have in Egypt or Assyria from the era). Where would one even hunt for such artifacts, and why would you expect there
were any artifacts for Abraham? I sense that you misunderstand archaeology. The absence of names from the extra-biblical, archaeological historical record is very much to be expected, and is in itself inconclusive. Lack of historical or archaeological evidence does not prove a character didn't exist or an event didn't happen.
I guess that's my biggest question:
Since Abraham was a Bedouin, and not a king, and never lived in a city, nor held an official position of any kind, and lived 4,000 years ago, why would you expect there were any artifacts for him? And what would you expect those artifacts would be?Here are a few things we know.
* The name Abrum is affirmed in Old Assyrian texts from the same era. It was a place name, but that would show that Abram's lineage could be associated with the region of Syro-Mesopotamia, as the Bible says.
* The details of the Genesis account during the life of Abram (Abraham) are astoundingly accurate and fit perfectly with the era and the region (things like Hittite contracts, the war of Genesis 14, the people groups around, descriptions of religious practices, etc.). If Genesis were written during the exile, as some claim, these details would have been unknown to them. We know about them because we're digging up stuff from the era that had been hidden for a millennium before the exile.
* Abraham and later Isaac are said to have made a treaty with King Abimelech, and Jacob made a treaty with his father-in-law, Laban. Over 90 treaty documents have been found, dating from 2600-600 BC, and these treaties take distinctive form from culture to culture and generation to generation, with oaths, curses, and stipulations being given different emphases and presented in different orders. The ones with Abimelech and Laban fit exactly the region and eras that Genesis puts them in, and not at all the later or earlier ones. Later writers would not have known this. It speaks to the historicity of the text.