Well, many people would say that they have discovered that supernatural person by way of their hearts. I would be one of them. Certainly none of us have proof beyond our own senses, but let's face it, everything is perceived by way of our senses. Hence, when a large group of people share the same experience, especially over a long period of time, I'd definately call that a kind of evidence.
What you don't understand is that you haven't got what's necessary in a laboratory situation to test the supernatural. If He's not there then youp obviously can't test Him. Even still, that obviously that doesn't mean He doesn't exist. I think that's a good example of virtually any concept that's tested in a laboratory setting. If all the necessary variables aren't present, then whatever's being tested won't produce an accurate result. Right? Hence, your test results will be invalid.
See, if there is a supernatural aspect involved, then you can't possibly arrive at an accurate conclusion without taking it into account. And there's no way you can ever be sure that supernatural aspect isn't involved; hence, you can never be sure your results are accurate.