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It seems to me many paranormal stories (like possession, or demons on Earth) just begin with the paranormal, period. In The Exorcist a child is possessed and must be cured. In The Omen, Damien (th...
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#3: Attribution notice added
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#2: Initial revision
It seems to me many paranormal stories (like possession, or demons on Earth) just begin with the paranormal, period. In The Exorcist a child is possessed and must be cured. In The Omen, Damien (the child) is the son of Satan and the Antichrist. To me most paranormal stories begin very early with a pre-existing paranormal thing and the protagonist is already aware of the paranormal, isn't surprised, doesn't need to "learn" about it, but is an expert that seeks to solve the problem and dispel the paranormal. Even in Stephen King's Firestarter, the father knows from the beginning what his kid can do, and is fighting to protect her. Those don't sound like either of your two scenarios.