Then there are those, like myself, who are the "Good Lord, it's morning" type. I have never been a morning person. I think it was programmed from birth since I made my "debut" late at night. Having begun life as a night owl, it set the pattern for life.
Although as a child I had to get up early for school, and as an adult for work, when left to my own devices (ahh, those blessed weekends) my body wouldn't rouse from slumber until around ten o'clock and would be ready for sleep sometime around 1:00 a.m. In college, however, I remember actually having to take NoDoz (the caffeine equivalent to several strong cups of coffee) in order to stay up past one o'clock to study for an exam the next day or to finish a term paper. Later in life, I developed chronic insomnia and my day shifted to the equivalent of a third-shift schedule which means I'm up most, if not all, of the night and sleep through the morning and sometimes into the early to mid afternoon.
This means that, for me, the most productive hours are between midnight and 3:00 a.m. It's not unusual to find me busy folding laundry, making out grocery lists, paying bills, etc., all during the hours when "normal" people are lost in slumber. It's also the best time for me to write. During NaNoWriMo, those hours often extend to between six and seven in the morning.
A few years ago, Neil Diamond wrote a song called "Thank the Lord for the Night Time." It should be my theme song. During the day there are too many distractions and interruptions for me to be able to concentrate on writing: the phone rings, the dog needs to go out, the cat wants attention, my husband needs to ask me something or wants to show me something, there are noises outside from cars, people and their kids. But after midnight, all of that stops. The phone is silent; the dog, cat, and spouse are asleep; the cars are quietly parked; people and their kids are snoozing. Yes, Neil, thank the Lord for the night time, indeed.
When it's dark, and the world is quiet, that's when I can concentrate and the creative juices seem to flow. Perhaps for you, it's the early morning hours before anyone else is up. Or it might be the afternoon after lunch and before the kids come home from school. The important thing is to find a time that works for you, then block off that time for writing. Morning, noon, or night time--whatever is right for you is the "write" time.