I love it when this topic comes up.
Its 300 years from now, the starship can sit at a poker table and deal cards...this fictional tale is set in the future. Who knows what will be possible tomorrow where impossibilities today are concerned. 300 years ago we shit in holes and thought skin color meant something. 500 years ago we thought the world was flat.
300 years from now we could put on gloves that allow us to pick up a cadillac. I remember when TNG came out, Trekkers and non-trekkers had a tough time with the no buttons thing. 26 years later, sometimes you can't find a button to save your life!
Oh yeah, they flew in at night. Scotty asked why have they been there since last night. He wasn't refering to the ship's internal cronometer I mean come on...this is the JJverse. Who knows, they went under at a distance, then had the ship swim up to shore to offer a better resource to the ground efforts. Cause of the emergency there was no time to swim out, ascend, then fly back and hope Spock isn't fryed.
The way I interpreted it was that they were there in orbit on a survey mission doing all the appropriate things which lead to them finding out about the volcano. From there they decide to put a plan in motion, and go over the scenarios. Because of the prime directive they do it quickly and quietly, which is why some of the crew including Scotty are wanting to know why they have been there since last night.
But one thing did get me and that was the size of the Enterprise. I really don't care how big she is due to the above mentioned reasons but it shows them swim up to the hatch and that hatch doesn't look any bigger than the hatches that the shuttle pods connect with in TMP, TWOK. When I saw that I remember thinking they may say she is 700 or whatever meters long but she is the same size as the original.