You have said Mary and Elizabeth were cousins, which normally suggests common grandparents. How could this be if Mary was of the tribe of Judah and Elizabeth was a Levite? Also Elizabeth was so very much older than Mary.
I was using the term cousin in its widest sense. Both Mary and Elizabeth were descended from the same man, Jacob. Mary came through Judah while Elizabeth’s ancestor was Levi. Judah and Levi were brothers. That makes Mary and Elizabeth cousins, though many times removed.
In any case the angel Gabriel called them blood relatives (Luke 1:36). The Greek word Luke used refers to a kinsman, and is translated cousin in the King James version of Luke 1:36.