Mission Availability Date

We've heard that it is possible to put your availability date before your birthday if you will turn 19 in the mission training center, is there any truth to that? I can only find that she can turn in her papers 120 days prior to her nineteenth birthday.

I've heard of missionaries who had their birthday while in the MTC, but I think it's an exception rather than a rule.

See https://www.lds.org/callings/missionary/faqs. The answer you are looking for is in the question "How early can I submit my missionary papers?"

The earliest date women may enter the MTC is after their 19th birthday.