Priests who could not find their family records had to wait for a priest who could consult what?

Answer: The Urim and Thummim

Excluded from the priesthood as unclean, they could not eat the most holy things until a priest arose to consult the Urim and Thummim.

“These men searched for their family records, but they could not find them and so were excluded from the priesthood as unclean. The governor ordered them not to eat the most holy things until there was a priest to consult the Urim and Thummim.”— Ezra 2:62-63 (BSB)