I've seen them start boarding as early as 11:30, but usually sometime around noon. They tell you not to start boarding until 1:30 because that's when you can get into your stateroom. If you board prior to 1:30, they'll usher you to the Lido Deck, where the buffet is and it will be very crowded with everyone sitting around with their carry-on luggage waiting for the announcement that the staterooms are available. Needless to say, it's noisy and crowded, plus everyone is pushing and shoving trying to stuff food in their mouths.
Personally, we much prefer to board around 2:30. No lines, no hassle, no crowds, and we can go right to our stateroom and then to the buffet without all the pushing and shoving.