You should give everyone enough time to buy a secret Santa gift, so you should start secret Santa about two weeks before the final gift exchange.
You can also do a secret Santa exchange any time of year (although you might want to change the name!) If you and your friends are all celebrating a milestone birthday, or a fellow group of moms that all have kids graduating high school one year, or you just want an excuse for a fun book club celebration – any of those are a great reason to have a secret Santa exchange with some friends.