For me it was in the early 1960's. Mom and Dad would take us up to Stokes State Forest and High Point in NJ and we would hike short sections. I was always fascinated that a hiking trail could go from Georgia to Maine. We did the High Point section a few times and it was a completely different and tougher trail that went up what appeared to be a rock wall property line (N to S) and the trail went right to the monument. Also, as a child we walked thru the Bear Mountain Zoo which is also the AT trail. That may have even been in the late 50's.
About 1964 or 1965 I went to a Boy Scout camp for 2 weeks called camp Wawayanda in NJ and 1 day a small group of us scouts climbed up a ridge and hiked along the Appalachian Trail.
So... probably I first set foot on the AT in 1958 at 8 years old at the Bear Mountain, NY park.