Under all that rock, it was a miracle the transporters worked ... It's even easier to conceive of a skeleton crew of refugees from the 20th century lacking the competence required to notice the life-filled bubble scores of meters away from the center of attention.
The writers pre-established that sensors could not detect the Genesis cave. Enterprise's sensors didn't detect it either. While it's an example of sensors working at the power of drama -- perhaps there were Plot-Convenient Deposits above the cave -- both ship's sensors play by the same rules throughout the film and Khan's motivation does not
change. Bill is just wrong on this one.