Short Answer:
Not through empirical science alone, but through a cumulative rational investigation.
Science is one of our strongest methods for studying measurable physical reality, yet its procedures already presuppose the external world, logical inference, and generally reliable observation.
It cannot use those same procedures, without circularity, to prove every presupposition on which it depends; nor is it designed by itself to determine whether physical reality has an ultimate, transcendent ground.
Example: Science cannot use empirical methods alone to prove that the external world is real, because every experiment already presupposes that world.
We should therefore combine metaphysical and philosophical reasoning with relevant scientific evidence, rigorous investigation of alleged extraordinary events, historical evidence, and critically assessed testimony.
“Proof” here means a publicly defensible conclusion warranted by the total evidence—not infallible or mathematical certainty.
Example: Every day, physicians make life-changing decisions by combining medical history, symptoms, physical examinations, laboratory results, and imaging: no single item may prove the diagnosis, yet their convergence can justify treatment.