This reminds me of one broadly similar, which also reminds me of one somewhat different.
Many years ago, I was walking with a group in Glen Coe. It was not a hike, just an hour or two's amble. One of the group, who was walking head down and just making conversation said, "I think you're meant to see golden eagles around here."
I looked up and far above me, a golden eagle soared out into view from over the top of the cliff. I said, "Yes, look, there's one." Everyone looked up and saw it, then it soared back out of sight.
Now, truth be told, I cannot be sure it was golden. However, it was certainly an eagle, and it showed itself exactly on cue, to the second.
The somewhat different case: I was on a school trip to the North York Moors. There were probably 20 of us, ambling along at very different speeds, with the faster group waiting every so often for the slower walkers.
We stopped on a bridge which, as I remember it over 40 years later, was over a disused railway. Being teenage boys, we started throwing stones.
One of the lads said to me, "I bet you can't hit that bottle," and pointed to one far below and some distance along the track. I said, "What, that one?" as I threw a stone and hit it, just like that. I was never an especially good thrower, and it was pure luck, but I have never felt more cool.