Oxygen levels are the same throughout the flight - irrespective of the cabin altitude. It remains at 21% of the air, what does change is the air pressure. As you climb up through the atmosphere, the pressure drops such that by the time you reach c18,000 feet the pressure has roughly halved, but at this altitude there is still 21% oxygen in the atmosphere.
Oxygen makes up 21% of the air and therefore makes up 21% of the air pressure. Air pressure at sea level can be measured in many ways but at sea level is usually 760mm of mercury - 21% of that is 159mm of mercury - this can be called the partial pressure of oxygen.
Your lungs work on a pressure gradient. There needs to be a greater partial pressure of oxygen in the air than in your blood for them to work. As you climb the air pressure (and with it the oxygen pressure) drops and the pressure gradient lessens. As you get to approx 10,000 ft most normal people need some assistance in breathing and above this it starts to become important. By 18,000ft or so you need oxygen adding to the air to boost this partial pressure, above 33000ft this oxygen needs to be given to you under pressure.
So as you can see, at sea level before take off there is no reduction in the oxygen in the cabin. Indeed there is not really a reduction in the oxygen level as you climb but rather a reduction in the pressure gradient between the air and you blood.
You sleep because you are warm, comfortable, have a lot of sound around you and your senses are being overstimulated and you are immobile. If you want to make a baby sleep, put it under a lamp, turn on the hoover and rock the cradle - bingo! sleeping baby.