Science uses reason, experimentation, empiricism, replication, etc., to study reality. We aren't limited to studying natural phenomena unless you limit the definition of "natural" to that which can be studied by science, in which case the claim becomes a tautology. Science studies supernatural claims all the time – esp, psychic clairvoyance, ghosts, near-death-experiences, miracles, you name it.
God exists, then either God has an empirically detectable effect on the
physical world, or he is irrelevant to human nature. Claiming that God
is somehow knowable through human experience and/or evidence and reason
but is utterly undetectable to the tools of science is tacitly admitting
that God doesn't matter and doesn't do anything, and the only thing
worse for religion than a non-existent God is an irrelevant one.