How quickly can I pass my Driving Test
3 weeks minimum once you have your provisional licence
The quickest way is to apply for your provisional licence 3 months or so before your birthday, when you receive it you can then apply for your theory test which will can be booked for your birthday.
Naturally as you have spent plenty of time revising you pass and as such are in a position to book a Driving Test.
Normal test waiting times vary from area to area but are in the order of 3-6 weeks which is probably the sort of time that it may take to develop the experience & skill to pass it comfortably.
However if you're really keen, and can take say 2 lessons a day from you're birthday, you could within 2 weeks be ready to get and take a "short notice" test that can often be booked within 2/3 days of application.