As Kimber stated, the answer is no. As we found out ourselves, under the current methodology the application cannot be inputted into the computer until the applicant turns 16. I'm guessing the computer won't allow a date under the age of 16. Worse, you cannot book the MSC course until you have you FAL "reference number" - which eventually becomes your FAL number.
Given NZ Post are generally shit at doing that one job they exist for - getting post from A to B quickly - we got the photos, documents and application fee sorted out 2 weeks before my daughter's 16th birthday and sent the application in one full week before her birthday, figuring it would take at least one week to take the three hour journey by road to Dunedin. I was right. We received a confirmation letter from the Police about 2 weeks later acknowledging receipt and containing the above number you need in order to book the MSC course.
When my son did his FAL a couple of years back he sat the MSC course 6 months before his birthday, sent in the application 2 months ahead of his birthday, rang the Police on his birthday to get the application moving and had his interviews within 3 weeks of turning 16. He was keen. Them days are long gone.
Of course filling out a 36 page application form makes the system SOOOOOOO much safer than filling out a 5 page application form because we all know bureaucracy thrives on lots of paperwork. We also all know that 36 pages makes diddly-squat difference if the police fail to carry out their job in accordance with established procedures.
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