I don't think there's anything any one person can say that will prove these things to you. I know there probably wasn't for me before I started to have my own experiences. I'd taken lots of psychology courses, I knew all about confirmation bias and it was really easy to take any of these stories and attribute it to coincidence or any number of cognitive biases our brains are prone to. But I was reading these stories in such quantity (not just in this sub but in other places) that it was enough to make me really wonder if there could be any truth to it, so I decided to try it out for myself, and that's what I advise you to do too.
Just think of a series of experiments you could do that would prove to you personally that there was something to this. If you believe you have a chance of winning the gold medal anyway then that's not a good experiment. From what I've seen it's best to pick something you know for a fact rarely happens to you, preferably something you don't even care about since it seems to be a lot easier to do this when you don't have resistance to the situation one way or the other. Most people here seem to choose the owl exercise in the sidebar (switch to a dimension with more owls).
When I first did this, to prove it to myself, instead of using owls I used something I felt would be more odd that I don't remember ever seeing but I knew existed somewhere, a pink dolphin. I meditated on this for 5 minutes a day for a while for about 5 days, and in those 5 days I saw a bar or something in the background of a tv show with a sign over it that said "the pink dolphin" and I saw a picture of an actual pink dolphin in an advertisement. and then about a week later, there was a story on a news site I go to about these pink dolphins that live in south america.
So could that have been a coincidence? Yeah but it was pretty crazy and enough to make me try doing it more. So I picked another weird thing and kept trying. And it kept working, and I'm pretty damn sure I'm getting better at it. I've been trying at this for about a month now. I started writing down how many times I was actually seeing the things I was meditating on so I could know if I was just exaggerating it all in my own head. My most recent experience: two days ago, I meditated for 10 minutes on dragons. That same day two people completely unrelated to each other separately mentioned dragons to me. Yesterday, I wrote down 5 separate instances where I came across dragons, I won't bore you with the details, but today I've already come across 2 other separate instances. After doing about 4 of these experiments and having them come out like this, each one better than the last, there's really only so much you can chalk up to coincidence. I mean you could make the argument that I've always been seeing this many dragons and just not noticed it because I haven't been looking, but that just doesn't seem like the most likely explanation to me anymore.
I know I'm just an internet stranger and everything and could be lying. So if you really want to know if there's truth to this, I'd tell you just pick something and meditate on it for 5 minutes a day for say, 2 weeks. In that 5 minutes imagine what it would be like to see, hear, feel, even smell the object you're meditating on in as much detail as you can, and most important imagine the emotion you'd feel if you saw it in reality.
Sorry for the length but I'm pretty excited about this right now. Just see how often whatever crazy thing you're meditating on starts to appear in your world. At worst you lose about an hour of your life, at best you realize that you're controlling the reality you see with your own mind. So it's up to you to try but it's the only way you're ever going to know for certain.