We have had children do this in the past. Your director can work with you to set it up, but essentially you would list your child as their own Authorized Pick-up person. We usually encourage families to set up days / times for when the child can check themselves out (i.e. any day after 4pm, Mondays at 2pm, etc). We do require that the child let us know they are leaving and go through our official check out process - if a child fails to do this we will need to reevaluate if we can allow them to check out on their own.
Additionally, we encourage parents to come up with a routine for this (i.e. call home when they leave, text once they are home, etc).