IT'S NEVER TO LATE!
I am often ask when is the best time to book newborn session. We newborn photographer often say the best time is till 14 days because that's when usually the baby is most sleepy, but it is not always the true! Some 6 weeks old baby can sleep trough all session where 5 days old baby will be awake from beginning till middle of session.
The key to have a successful newborn session is to have a newborn posing flow and know how to navigate session when baby is awake. I learn my workflow and know how to position baby, when to swaddle to I can have sleepy baby in minutes. It takes time and experience but I can work with usually baby till 8 weeks and still get nice picture families will treasure forever.