How long had Mary and Joseph traveled before they started looking for the boy Jesus?

Answer: A day

Assuming he was in their company, they traveled on for a day before searching among relatives and friends.

“When those days were over and they were returning home, the boy Jesus remained behind in Jerusalem, but His parents were unaware He had stayed. Assuming He was in their company, they traveled on for a day before they began to look for Him among their relatives and friends.”— Luke 2:43-44 (BSB)