Obviously, this is an entirely academic exercise that really has no bearing on the international legitimacy of modern Israel. But it seems to me that many (American) non-Jewish supporters of Israel try to build some sort of hyper-Biblical legitimacy for the modern state of Israel by appealing to God's promise to the Jews of the Old Testament, without bothering to understand what an Old Testament Jew is.
It also, to my mind, points to a strong hypocrisy in Israeli policy and the difficulty created when you try to maintain an ethno-religious national identity. Israel requires people to take a DNA test to prove their Jewishness before being allowed to make aliyah, when the truth is almost nobody in modern Israel, including the policy-makers, qualify as true Old Testament Jews.
This claim that Jewish Eastern European ancestry is not from Israel, is false, and has been used by those opposed to the existence of Israel.
Previous to DNA information, the movement and ancestry of the Ashkenazi (Eastern European Jewish people) have been well known. Transiting from Italy, concentrating in the upper Rhineland, at the time when Charlemagne invited them around 800. They grew in number there, and spoke a language partially Hebrew and partially German called Yiddish. They wrote that language in the Hebrew alphabet.
At the time of the first Crusade in 1095 there were massacres and expulsions against Jews in the Rhineland area. At the same time the large Lithuanian Empire, later the combined Polish Lithuanian nation, wanted Jewish immigration. The Ashkenazi people moved in mass from Germany and France to what would later become the Baltics, Poland, Ukraine, Belorus, Moldava, and other nearby areas.
The Khazars, whose nobility converted to Judiasm in the 900’s, were never converted in large numbers, and were not an existing Jewish nationality by the time that Jews moved to that region in the 1100’s. People who try to deny a Jewish connection to Israel often bring up the Khazars.
DNA analysis shows not only Jewish ancestry by Ashkenazim, but also for those who are Cohens (paternally descended from Moses’s brother Aaron), a unique marker.
Ashkenazi Jewish traditions, and ancient Rabbis often quoted, show the places as well. Moving between the places described above.
Furthermore, half of the Israeli Jewish population is Sephardic, who lived in areas from Spain to Iran, and maintained their religion through many centuries of Islamic rule. They were all forced to leave their homes after Israel was created. They didn’t become refugees, demanding to recover their homes in Arab lands. Instead they helped build a new nation in Israel.