I agree, the sooner the better. It is important to realize it is a 1st come, 1st serve basis. They have a limited amount of time for the board, and there is no promise that they will get through every application on file during that board.
For example, they have 3000 files to review for that 1st board, but only can get through 2999, and you are no. 3000, your packet will be deferred to the next month. You will be no.1 on their next review.
Not only that, BUT, and a very important BUT, you also maybe deferred to another board because at that time your scores are on the cusp, and they are waiting to see how you rack up from a larger pool to review. This is why it is important to update your file with any new awards, SAT scores, etc.
Not everyone will get it on their 1st shot out (board wise). They will inform you if you have been deferred. When our DS went through the process for class of 12, his ALO actually contacted him and said okay you will be meeting this board. I do not want to swear, but I believe he was told the cut off day was not weeks before, but about 1 week prior. I think he had to have everything in the Friday 1 full week before the board met. For example, if the board is meeting the 6th of Dec, he had to have it in by the 27th of Nov.
Things change though so don't take my memory for granted, contact your ALO for current info.
Good luck...AIM HIGH!