Your blood glucose level is going to rise and/or fall during the morning, depending on a number of factors, from fatigue, stress, activity levels, how hot your shower was, how long you are up before you test, etc. etc.
So you really need to just pick a time in your routine that it makes sense, and do it consistently then.
You will be able to see trends that way, and the odd rogue reading will probably be identifiable (yup, that was the day we had the car alarm go off down the road that woke me, or, yup, that was the day I had a job interview).
My own blood glucose will rise by 1-2mmol/l between opening my eyes, and finishing in the bathroom. Then it will continue to rise steadily until I eat something. So if I want a low reading, I test on waking, before my feet hit the floor, and if I want a high reading, I wait til I am downstairs and about to eat. They are both fasting readings, but experience has taught me that they tell me more about activity and stress than about my overall diabetic control.