Entry to the Duomo starts every day at 8 am, but it's best to arrive before that if you want to be one of the first to get inside. Flash your Milan Cathedral tickets then and you might have the roof to yourself for a while! The church itself stays open until 8 pm. The last admission up to the roof terraces is at 7 pm.
If you can, visit on a weekday. Weekdays are a lot more tranquil than weekends when all the tourists seem to descend at once.