If 'first experience' means 'first ride', mine was my parents and I being driven from Idaho to Salt Lake City by my grandfather, to board the westbound CZ (when it still used the UP station.) I was disappointed I couldn't ride Pocatello-SLC first, but nobody else but the little boy wanted that enough to suffer an 18 hour layover in Salt Lake.
Departing Salt Lake required an odd reverse move, which resulted in us sitting in the street in front of the Rio Grande Station for several minutes. I looked out the window and thought "gee, how silly that we aren't using Rio Grande Station" -- and a year or two later, we were.
We were seated in the coach-baggage car, and by the next day we had learned to make a beeline for the coaches rather than the coach-baggages (which as-delivered had the seats several inches closer together.) I hardly slept a wink, peeking out the window at moonlit desert and being woken back up every time we passed a freight train if we dozed off.
Somewhere in middle-of-nowhere central Nevada the next morning we stopped to pick up a tour group of 20 or so. We were a little late already and were close to an hour late after that unscheduled stop was finished. Soon after had my first helping of dining car French toast, and first time in the Superliner lounge going up Donner Pass. I tried to take photos but mostly I got reflections of the inside of the glass.
If experiences includes things other than rides... the first time I SAW an Amtrak train was - truth is stranger than fiction - camping somewhere in western Montana when I was 3 or 4 years old. It was after dark, something had gone amiss with cooking dinner over the campfire, and my dad was trying to make popcorn, in one of those old electric pour-the-oil-in-first poppers, using the one electric outlet in the men's restroom for shaving. We heard a train going past and stepped outside to look; it was the NCH. It was dark but I could see the sides were shiny, see a couple lights on the outside of each car, a few ghostly-lit-up windows...
Some years later we chased a few nearly-Superliner-equipped CZs through eastern Utah on family trips to the southewestern national parks, and got to go inside an exhibition train that Amtrak parked in Salt Lake for some reason or another the same day we drove through town.