How?
The Jews of Jesus time knew what tribe they were from....
When the Jews were dispersed they inter-married with gentiles, so I don’t know how we could really have a accurate image of the Jews in Israel during the times of Jesus.
The 'lost sheep of the House of Israel' were NOT there when Jesus walked this earth. (Matthew 10:5-6) They had been sent into captivity hundreds and hundreds of years before the event of Christ walking in a flesh body. What had returned was the House of Judah which also included the tribe of Benjamin, which is the tribe that Paul states he was.