We have a castle built in the 19th century that was demolished and rebuilt in the early 20th century. The castle's name still comes from the family that built the first one. Which build date should `start_date` hold?

We have a castle built in the 19th century that was demolished and rebuilt in the early 20th century. The castle's name still comes from the family that built the first one. Which build date should `start_date` hold?