Your port arrival appointment that you chose when you did online checkin is all you need to worry about. Usually when parking first opens, the traffic flow workers turn away folks who are obscenely early. But enforcement of that varies from week to week. Generally the lines at Charleston are pretty good these days, they were bad years ago but they've made great gains.
I believe you can prepay for parking on the SC Ports website via credit card, or pay when you arrive at the pier on embarkation day. If you happen to have a handicap placard or plate, parking is free per SC law.