I tried to make an appointment, I was told that the site refreshed every 15 minutes, after waiting in the non-appointment line for nearly 9 hours. The best time to go, with out an appointment, is about 530pm. At that time I only waited about 30 minutes. I'm not sure about the learner's permit.
Regardless of age, you have to get a permit to take a driving test, so yes you can have a permit at 23.
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