Major spoiler alert:
It made plenty of sense to me in light of the fact that the older Spock has full knowledge of Kirk’s lifetime in the other timeline.
Well, And Captain Pike did make Kirk acting first officer to Spock. The thing that some detractors seem to be missing was that Pike told Kirk in the Bar that Star Fleet had lost its edge, and newer fresh blood with high energy initiative was needed to invigorate the officer corps(not the exact words but that was what Pike was conveying) I got the sense that the Star Fleet in that time line was in danger of losing it’s edge, its purpose...at least Abrams was trying to convey that notion. The “disaster” caught Star Fleet at the ragged edge with few ships and experienced personnel to deal with it.
I beleive there were a lot of quick promotions and battlefield commissions in WW2, especially at the beginning.
The great strength of the Americans was that they responded way beyond their expected capabilities in these new rolls as a whole, as did our women on the home and factory fronts!
So I could believe an inexperienced command crew, yet imbued with drive and a sense of mission, could pull together quickly in a time of crisis, even in the 23rd century!