I "think", from talking to a SS fellow, that you can apply in Dec to start your SS in January.
You don't have to show up January 1st , and tell them "start me today" .
The local SS office set my phone "interview" for a January start --Nov 15.
Not saying you could not wait until later but personally I would not want to wait pass Dec 15 to apply for Jan.
Nwsteve