We have no historical references to him from his time period, and according to the much later stories about his life, he never really interacted with any group of people who had writing to any sort of extent that would have led to him being written about. So there wouldn't be anything written about him if he were a person who existed.

It is extremely difficult to find any sort of evidence for a specific person existing prior to the invention of writing. Unless they were important enough to be a major player in international politics (to be mentioned in another king's records), there is virtually no chance of any individual being recognized during the proto-historical periods in areas without writing. While writing certainly existed in Egypt and Mesopotamia during the time attributed to Abraham, it was not something used in the in-between more frontier lands that Abraham traveled in.

We cannot say one way or the other whether or not Abraham existed. We have no direct evidence he did, but it is impossible to say that he didn't, because there are no records in which he should appear. In Biblical terms, everything prior to David is in the same boat, prior to the adoption and use of writing. We can't say for sure whether or not it happened, as it isn't recorded anywhere for the simple reason that there just was no writing in which to record it, and the events that happened in places where there was writing (such as Moses and the Exodus), turns out that they knew about the power of writing and recording for posterity, and manipulated it so hard, and often twisted events to make them sound better and even straight up erased people from history or retconned their own past (a la Lenin and Trotsky).

So it's basically a useless discussion to try to determine whether a Biblical figure prior to David is "historical" or not, for the simple fact that they would not have ever been recorded. And without a record, we cannot "prove" that they existed. We believe the great Greek philosopher Pythagoras existed (Pythagorean theorem and all that), but there are no contemporary accounts of his life, and there are no details of his life in later works that are not contradicted by other writings of roughly the same time. Picking out individuals in ancient history who left no writings or are from times where there are no writings is incredibly difficult. Finding proof of certain individuals even in periods with lots of historical records can sometimes be very difficult.