During the E3 play-through, they specifically skipped the initial part of the game where you would've first moved in, picked your starter, battled your rival for the first time, etc. They could've just skipped this for time-purposes as they stated, but couldn't it be possible they did it for another reason as well?

Just like the Japanese kid in the initial trailer that came from a faraway region, I believe the protagonist parallels that. And that region, based on my own thoughts, is Kalos.

This is why they skipped the initial part of the game. The protagonist boarded the pictured train with his mom to the docks on the exterior of the region, where they then took a boat to Alola.

I believe in the postgame, we can take a boat back to Kalos and then take that train back into the interior of the region.

Completely unrelated to this theory, I also believe that you receive your starter because Tapu Koko shows up when you arrive, which impresses the fat professor and prompts him to give you a starter.

There may be more, because we've never had a starter given to us without a bit more reason. Tapu Koko showing up wouldn't be enough.