^I haven't seen the movie yet but it is my understanding that the blood cure hardly comes out of nowhere.
Isn't it introduced to the story from the very start of the movie with the little girl and later in some kind of tribble experiment? Or am I wrong?
It does pretty much come out of nowhere if you haven’t been reading the spoilers. I’ll address the two points that you consider to have set up the blood cure.
First, the little girl. What we know is that the little girl is sick, doctors can’t help her, then Khan gives the father a drug that cures her. This lets us know that Khan has some kind of wonderful drug that is not available to 23rd-century medicine. The drug is the color of movie blood, so that might be seen as an indication that Khan’s blood is the special ingredient that will enable 23rd-century doctors to reproduce the drug, but it’s a pretty big leap for someone who doesn’t go into the movie already knowing it to be the case. There is certainly no reason to expect, at this point in the movie, that the wonder drug can not only cure a sick little girl but also reanimate the dead (even when the cause of death doesn’t seem to be related to the girl's illness).
Second, the tribble. McCoy says that Khan’s cells are extraordinarily resilient, and he injects a sample of Khan’s blood into some necrotic tribble tissue in the hope of learning something about the mechanism. It’s not until after Kirk’s death that the necrotic tissue sample turns into a living, breathing tribble.
If you go into the film already knowing about Khan’s blood and how it will ultimately be used, then those two scenes are easily recognized as related to what you already know is going to happen. But if you don’t go into the film already knowing that Khan’s blood can reanimate the dead, the tribble waking up is the first sign of its resurrectional quality.