One day when I was a Christian I was praying to God and saying, "God please let me meet somebody to witness to today". Later that day a man just walked up to me out of nowhere and said, "If your religion goes bad do you go bad with it?" I said "No" and he said "Thank you" and walked off. I had always wondered if there is no God, how my prayers got answered when nobody heard me praying that day in the car since I was praying under my breath and the doors were closed.
It's an interesting story, but does not impress me as an outside observer as much as it obviously impressed you when you were in the situation.
People in general are notoriously bad at calculating the odds of an event occurring. Events which strike us as "unlikely" are actually fairly commonplace, especially because we are able to invent patterns and attach significance to a very wide range of possible events. For example, the request you made was extremely unspecific, and could have been fulfilled by all kinds of different things happening over a long period of time. You said that the person came up to you "later that day," which doesn't make it nearly as interesting if, say, you had prayed and somebody had shown up immediately. And "meet somebody to witness to today" isn't all that specific either -- you might well have tried harder to push some kind of religious topic into any conversation you had that day, and seen it as scoring a hit. The witnessing you actually did in the end (you were asked a question and you gave a one-syllable answer) doesn't strike me as especially significant, although I'm sure it struck you that way at the time.
People are also very susceptible to confirmation bias. Stuff happens every day that does not seem significant, but when it matches some kind of expectation we have, we tend to notice that one event and attach special importance to it, while ignoring all the other things that didn't fit our conception of something unusual or miraculous. For instance: in your story you didn't specify if that was the only time in your young life that you ever prayed for anything, but I bet it wasn't. And I'll bet that you didn't waste too much thought on all the times you tossed out a casual prayer and nothing happened.
If you wanted to do a real test of the power of faith, you shouldn't need to say "God, please cause [some fairly commonplace event] to happen before [some fairly long span of time] has elapsed." You ought to be able to say: "God, please let a bird with blue spots and a crooked beak fly past my window within the next ten seconds." If something that specific happened in that small time span, that would be interesting. If you could repeat this demonstration of the effectiveness of prayer multiple times consistently, that would be really interesting.
As it is, the impression I get from your story was "I prayed for something just barely unusual to happen eventually, and on this one occasion it did." If that's the main reason why you're a theist today, then I think I can say with confidence that I could have experienced an identical occurrence and still not acquire your faith.