The assertion that all the genealogical records of the Jewish people were destroyed is untrue and unfounded. No such event ever occurred in Jewish history and there is no historian or ancient source that supports this claim. The genealogies of the twelve tribes of Israel were not stored in the Temple and they were never destroyed. Moreover, the majority of the Jewish people did not live in Israel during the first century and their genealogical records would have been unaffected by the destruction of Jerusalem and its Temple in 70 C.E.
With regard to personal genealogical ancestry, bear in mind that there is no segment of the Jewish people who are more aware of their tribal affiliation and more mindful to properly transmit this distinctive ancestry than the tribe of Levi. It has always been critical for members of the tribe of Levi to be aware of their unique place and status among the nation of Israel. This is true for a number of reasons. For instance, there are numerous distinct laws that apply only to this tribe. For example, there are certain women who a priest (kohen), who is a descendant of the tribe of Levi, may not marry. In addition, a priest is prohibited from coming into contact with a dead body. Also, only descendants from the tribe of Levi are involved in the Aaronic Benediction ceremony celebrated every festival throughout the world. Simply put, every family from the tribe of Levi is known to the Jewish people.
Moreover, not only are the descendants of Levi keenly aware of their unique ancestry, but the Jewish community as a whole has always been well aware of their identity as well. For example, only members of the tribe of Levi are honored with the first two blessings during the Torah reading in the synagogue. Also, any descendant of the tribe of Levi is identified as such on all legal documents such as marriage contracts and divorces.
Bear in mind that there were hundreds of thousands of priests and Levites throughout the Roman empire during the first century. They did not forget who their fathers were. It was always well known and meticulously documented by the Jewish people who their ancestors were. This information was carefully passed down from father to son and was often recorded in a family’s Sefer Yuchsin (a record book of family genealogy).
In my own family we have a Sefer Yuchsin that dates back to biblical times. In it every male between Aaron the High Priest (Moses’ brother) and myself is carefully recorded.
Rabbi Tovia Singer, HaKohen