No way, you tell them you're attacking on Thursday night/Friday morning at midnight. Then do a headfake, a completely impotent showing, but keep at it for at least three hours. Then let it fall apart as users drift off.
Then, around eight am, when the US gets to work, and anyone at Facebook who took you seriously is sleeping in after the late night? Then. That's when you pull out the big guns.
I wonder which hour of the day is their busiest... That would be my true target time.