Oddly, it wasn't until many years later that I put two and two together and realized that I had seen the first episode broadcast.
Yeah, growing up and watching the reruns on a constant loop in syndication, I doubt that most of knew (or cared) what order they were supposed to be in. I remember being scared by the Salt Vampire when the show ran one evening on NBC so I guess I must have that first airing, but it blurs in my memory with other nights watching Star Trek with my dad, along with The Twilight Zone, The Outer Limits, and Batman.
I don't think that I knew that "Mantrap" was the "first" episode or that "Turnabout Intruder" was the last until I started reading books and articles on Trek in my teens.
(Remember, there was no wikipedia or internet back then.)