Yes we can use did or had with the past sentence. Examples of Did are-
1. Did I hurt you?
2. Where did you come from?
3. How did you know you loved him?
4. Where did you leave the surface of the Earth?
5. What did she eat today?
Had examples-
1. They had adopted two children already.
2. She had a choice.
3. But they had no bouquets either.
4. My father climbed many trees when he was a child.
5. Miss Smita had had cough for days.