I think it's important to honor your own cycles. I notice, though, that once I've purged all the constant humming of my own mind, I can greet the day more peacefully.
I'm not a morning person either, in fact I'm quite crabby when I wake up so I force myself to wake up a few hours before my kids get up because I like greeting them with a smile. it's easier after I've been up and had a few cups of coffee, written my morning pages and had some peace. THEN, I'm happy to see them.
Before that point, they're noisy and move too fast and bounce too much and ask to many questions and can't do anything for themselves. A few cups of coffee and I'm happy to help, love to hear about their dreams and eager to help them get dressed, etc.
I force myself to be a morning person, for the health and safety of our family.
If it doesn't work for you, I'd grab any quiet time you can. When I purge my thoughts before bed, I sleep a lot better.
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