I see them all the time in the sky, I've watched them as a kid since the 70s.
Now with this magic thing called the computer, capable of complex trigonometry well beyond yours, you can actually predict when they will pass overhead and be observable.
https://en.wikipedia.org/wiki/List_of_satellite_pass_predictors
I used to occasionally catch the International Space Station, and sure enough, there it was in the sky, on cue. Then frequently you could see it pass into the earth's shadow and go dark. I had an app on my phone that even showed me what state it was over before it passed out of my sight.
That's what proof looks like.
