This is a bit unclear... not being critical but who or what group are we trying to prove paranormal events to? I find it ironic, just as an example, that "Christianity" especially will be loudest in voicing their disbelief in and disdain for anybody claiming to be "psychic". And yet, almost any mother will admit to an unknown connection, that transcends the physical, to their children that is clearly "psychic" in nature.... Mother's Intuition.
We have numerous examples in the Bible where mortal man interacted in some way with "God" or other entities. The story of Saul, who sought out the witch of Endor, so he could speak with the long-dead Samuel. The Bible records a conversation which is significant in a number of ways. The ability to connect to a soul who has passed beyond the Veil was a well-known art, long before this event allegedly took place. Deuteronomy identifies many of these "arts" that allow humans to communicate with incarnate entities, one of the reasons they were deemed such a threat to the church's authority.
Combined, this can lead to a very reasonable conclusion. There are numerous texts, both ancient and modern, where a belief in supernatural interaction is core to that religion's dogma and doctrine. If it has occurred before throughout history, common sense tells us that it is very likely happening today as well.