I can usually book an appointment the same day by refreshing the screen and choosing the location I want, in my case Ladson. But the same day and times disappear as fast as they appear, just keep checking back every 20 minutes or so.. good luck!
Stick to your appointment. When I went to renew my DL, I had to schedule an appointment. I did so online. At the location I was told my earliest time would be on the first (June). Going online I checked at other nearby locations, all showed being booked till the 1st of June. If you miss your appointment, you will have to reschedule, hopefully it won't be another 2 weeks or whatever!
Don't go there without an appointment, they are going to reject you and lose your precious time.
Unless it's changed the only way to get in is by an appointment
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