Given the info we've apparently had on Cosmog being a rare one-of-a-kind Pokemon that few locals know still exist and the Aether Foundation is researching, I'm still pretty sure Cosmog and the Cosmic Eye thing are in fact prevolutions of our box legendaries, with the Cosmic Eye evolving based on the version its in. (It will likely also have something in-game preventing you from trading it until it becomes Lunalla or Solgaleo.)
I originally made some story speculation long ago before Team Skull or the Aether Foundation were revealed and I think with this new piece of the puzzle I'm confidant I was onto something.
I believe the Island Trial was once an ancient ritual only a few select trainers occassionally went on, but nowadays has been modernized and turned into a challenge for the young trainers of the region very simillar to the Pokemon Leagues of other regions.
However, Tapu Koko revealing itself to us marks our significance and that we will be undertaking the Island Trial to fulfill its original, ancient purpose: Appeasing and paying tribute to the Sun / Moon and the Pokemon that acts as its emissary.
We won't be told its exact significance, but we will be given the choice to allow Cosmog to join us on our journey or not, watching our progress from afar instead. Our completion of the Island Trial will allow Cosmog to take its final form and bless the Alola region with life power and the proper passage of night and day until it is time for the ritual to be done again. Of course, this cycle is more important then the others due to Team Skull, The Aether Foundation and Ultra Beasts likely paying a large role in the plot and threatening the Alola region.