Well, I've had some very strange experiences in my life which I can't explain in any physicalist viewpoints currently known. Am I 100% certain that those experiences were supernatural? - I think I'm not! But, I suspect that there are things out there we can't see, hear or smell but sometimes we can feel the presence of those things around us.
For example, when my father died a couple of years ago, our dog didn't see him dead (father was living on his own) so she shouldn't have an idea if he's alive or not. Right after we buried him, the dog behaved very strangely on one particular day only. This happened before 40 days of my father's death. The dog never behaved that way prior to that day. She was hiding all the day and gazing at something where there was nothing at all. She was curious yet afraid of what she was experiencing. She didn't eat or drink that day, nor did she have reaction when I was calling her to come to my side. She switched her hiding places a couple of times throughout the day and no matter where she hid herself, she always looked at something where there was absolutely nothing at all (no flies or bugs or anything like that which dogs find annoying and try to catch).
She behaved like that for the whole day until my mother came in afternoon. She called her but the dog didn't react to her calling either which is absolutely unnatural as she always goes crazy whenever anybody comes in after being gone for a whole day. My mother too questioned what was wrong with her and I explained everything to her that the dog was behaving very weird that particular day. I forcibly moved the dog to the room me and my mother were chatting and placed her on the floor but she immediately run at the wall and sat there (there was no other place to hide so she felt safer sitting with her back against the wall). She was staring something right through my mother and out of the blue she started to shake her head with her eyes open wide. She shook her head a second or two and immediately run at my mother and climbed to hug her. After that she started behaving normally again and this strange behavior of hers never repeated again to this day (as I mentioned, nor did she ever behave like that prior).
I have had other weird things happened to me before that, two of which can be attributed to religious miracles but nevertheless, I was still questioning the god and the existence of Jesus Christ (more specifically, I was questioning him as the part of god and viewed him as an ordinary historical figure if assumed he existed at all which I wasn't quite sure either). Those events, although were inexplainable to me and had a profound effect to me at both times they happened, nevertheless, I forgot about them and moved on into my adulthood with no trust in god mindset (although I was still questioning everything and never excluded the possibility of the existence of god deep down into my heart).
There are other weird things that I find really odd to happen by pure chance that I experienced firsthand in this life so everything adds up in the end that leads me to think that there's something greater into or outside of this world we live in that can't be known with our human flesh senses.
