They can start laying any time of the day but the Hens in my flocks will generally lay a little later and later each day until they skip a day, then start early the following day and again goes the cycle. Keeping them locked up is a bummer, but not as much of a bummer as losing a Hen that's gone broody on a secret pile of eggs and a predator ends up nabbing her
I go thru this each breeding/laying season, so I feel your pain

