Ships usually state in their documents that boarding will begin between 1 and 2PM. That said, we are often onboard by noon or shortly thereafter because they are so good at changing over. We have gone by the embarkation area at 9AM in the past and observed people standing there waiting in line, why, I have no idea.
While we are often one of the first onboard and actually have been first onboard twice somehow, we do not show up before 11AM as that seems to be the time that they sometimes start. If not, then we usually do not have but an hour or two to wait at the most. Passengers often continue to board right up until sailing.