If you think the existence of Abraham is "undisputed", I suspect your information on Biblical archeology is very out of date. The general scholarly consensus is that there is no evidence of Abraham as an actual historical figure outside of the Biblical account, and that the accounts of the patriarchs are likely re-tellings of oral traditions or an invention.
"After a century of exhaustive investigation, all respectable archaeologists have given up hope of recovering any context that would make Abraham, Isaac, or Jacob credible 'historical figures." William Dever, What Did the Biblical Writers Know & When Did They Know It?
"We know about Abraham only from the Hebrew Bible since no other independent source of information is currently available, about Abraham either as a literary invention or as the creation of a collective memory the origins of which are now irrecoverable. Joseph Blenkinsopp, Abraham: The Story of a Life
"The actual individuals mentioned in the Bible probably did not exist…The travels and experiences Abraham experienced with his family as they wandered in foreign environments, entered the new homeland, and fled to Egypt are all enduring and engaging stories, reflecting the history of the late 10th to 8th century BCE, but projected back onto the characters of the patriarchal period" Bernard and Fran Alpert, Archaeology and the Biblical Record.
"There is considerable uncertainty whether the patriarchs in the Bible actually lived or are instead legends of ancestral founders. No evidence for their existence has been found independent of the Bible". Elliott Rabin, Understanding the Hebrew Bible: