I had never heard the term "first moon party" until I watched this video, which has gone viral over the past 2 weeks. Was the phrase just recently coined by HelloFlo's ad, or has the phrase been in use prior to that to refer to a celebration of a girl's first period? (assuming that people even have celebrations for a girl's first period...)
It wasn't coined for the ad.
Oldest reference on Google books seems to be from a novel Catching Heaven by Sands Hall from 2000.
"And I am not giving Hannah a First Moon party, or whatever it's called, when her period comes. She'd die of embarrassment." Jeep shrugged. "Maybe."
There's also this product from 1998: First Moon: Passage to Womanhood
A ceremonial kit containing complete instructions and the elements to stage a celebration ceremony to welcome the young woman to womanhood.
I have discovered that there is the word menarche, which is used to refer to a female's first menstrual cycle. Wikipedia says its origin comes from the Greek men (meaning moon) and arche (meaning beginning). Merriam Webster says the word was first used around 1900. This is most likely where the phrase "first moon" came from. I also discovered that an alternative for "first moon" is "first moontime".
The earliest mention of the phrase "first moon" I can find is in a 1976 issue of Many Smokes magazine, where it says the following:
When a young man had his first successful hunt, when a young woman had her first moon,
The earliest mentions of menarche or first moon parties I can find are the following:
Years and years and years ago before there were tampons or pads, girls would make their own "moon pads" out of cloth in anticipation of their first period. These would be washable, reusable pads they would use over and over again through the years. The reference to the moon had to do with the similarity of periods to the monthly cycles of the moon, although the moon has no influence over anyone's period. It made for a good reference to "that time of the month". So, that's kinda where the reference to the moon came from and why somebody might have a moon party.