I got my card last friday and bought AA gift card. Statement closed 11/26 and I received my 250 credit and new $250 credit will be available after 12/26 statement. The AA charge posted on 25th - so just a day before statement closed but it still triggered the statement credit.
As long as you get a statement in Dec you will be fine. I may be wrong but you cannot choose when first statement closes. You can change the due date/statement date but it takes upto 2 cycles for that to take effect as I learnt during the AA Exec 100K promo earlier this year.