That's actually the default behavior. The current options related to the CCS are "Classic Mode" which disables it entirely, and "We Didn't Start The Fire", which makes it exist at the start of the game and jump to being pretty dangerous.
If you don't use either of those options, the CCS doesn't exist at the start of the game, but will appear when the country becomes sufficiently Liberal. It begins weak and makes less frequent raids, avoiding direct confrontation with the LCS. If unchecked, the CCS will become more bold and powerful over time, appearing more often in the news, sending groups to attack your Liberals as they're on their way home from major missions, and eventually raiding or carbombing LCS safehouses.