I take a very scientific approach to the supernatural: I neither believe, nor not-believe.
Science isn’t about what to believe or not believe; what you stating isn’t a “scientific approach”.
The “scientific approach” is about testing a statement, explanation or prediction, that is formulated as together as falsifiable hypothesis.
The testing come from finding evidences or from test results of controlled lab-environment experiments. The evidences need to be at least detectable (or observable), measurable, quantifiable or verifiable, or any combination of the above or all of the above.
The more evidences (or tests performed) you have, the more you can determine whether the hypothesis “probable” or “improbable”.
By letting the evidences to determine outcome of the analysis and conclusion to the hypothesis, is how scientists objectively reach consensus whether the hypothesis is true or not, because it is possible that other scientists can independently perform the experiments or independently find their own evidences that will either back or refute the hypothesis.
That’s the “scientific approach”, the ability to test.
Science deal with “what is probable” or “what is not probable”, not what is possible or impossible.
The weighing of “possible” or “impossible” is the philosophical approach or the religious approach.
Scientists used probability to determine outcome, philosophers, religious people and mystics used personal belief to biasedly support their own agenda.
As to the supernatural.
There are no scientific approach to the supernatural.
Yes, scientists have tried to test the supernatural or the paranormal, but it has failed, and parapsychology (eg remote viewing) have been deemed to be pseudoscience.
The only people making money out of the supernatural and parapsychology, are novelists, tv and movie makers, and con artists (eg Deepak Chopra).
There are no evidences to support the supernatural.