I usually recommend newborn portraits in the first two weeks of life. This is when we can usually get the sleepy poses of them curled up like they are still in the womb. Sam was already 3 weeks old when his mom contacted me, but she really wanted to try for those sleepy poses, even though we had missed the optimal window. Thankfully I was able to squeeze them in and we took these on his one month birthday.
He slept through the whole session and his portraits came out beautiful!