This March 1972 newspaper article printed in The Portsmouth Herald talks about two local high school students who attended the first Star Trek convention in New York.

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From Fanlore, the fan run wiki about media fandom:

“The first New York Star Trek convention was held January 21-23, 1972 at the Statler Hilton and featured guests (Gene Roddenberry, Majel Barrett,Isaac Asimov, Hal Clement and D.C. Fontana), an art show, a costume call, NASA space displays (moon rocks and an astronaut suit), and a hospitality room. Episodes were also screened from 16mm prints, including the original pilot The Cage and a blooper reel.

The phrase “Star Trek Lives!” was used on the flyers advertising the first convention in 1972 and was part of the Star Trek revival campaign undertaken by fans in the early 1970s.

The organizers of “Star Trek Lives!” anticipated only 500 attendees. When 3000 fans showed up, by the final day of the event registrars were issuing ID cards made from torn scraps of wrapping paper and some fans were let in for free: “We ran out of everything,”Devra Langsam remembers. “We were cutting and sticking labels and pinning them on with straight pins.” [1]

“….[They] had expected about 500 to attend the convention. But, four hours before it was officially due to start, [Al Schuster] looked around at the mob scene on the 18th floor [of the Statler Hilton Hotel] and said, ‘It’s wild. We’re going to have at least 3,000 people here. They’re coming in from all over, Arizona, California, Canada. There’s a whole busload from Toronto.’[2]

undated photo of Gene Roddenberry addressing fans at a Star trek convention in the 1970s

An article in the Village Voice in 1972 describes the first convention:

"The convention was dreamed up and organized by three adult sci-fi freaks and show buffs, but it seemed to have been taken over completely by kids – they manned most of the tables and did most of the trading. Few people over 16 were in sight, but there were plenty of 10- and even eight-year-olds lugging around huge suitcases crammed with treasured nuggets of Startrekia, and they approached the business at hand with the same circumspection that’s evident at a big Parke-Bernet event. One pale, serious kid who looked about 11 approached another – 'Aren’t you that ”Dark Shadows“ freak?’ 'Yeah. Got anything?’ 'Some early glossies, to trade for Shatner shots only.’ 'So, let’s have a look.”[3]

In spite of what the outside world thought about fandom, fans were ecstatic to be gathering:

“The auditorium had seating for 500 - and 1500 crowded in to hear Roddenberry speak. Yet the event never got out of hand; Trek fans have a reputation for being well behaved, if exuberant, and this proved that it is one they deserve. The mood was exhilarating, and when Roddenberry spoke, the crowd exploded. Even he was surprised at the amount of love and appreciation for the series that the fans gave him. At one point, the fans even burst out chanting “Star Trek lives!” Suddenly it seemed possible that the series wasn’t dead after all.”[4

Even though the 1972 convention netted the organizers only $92.36 each (after expenses)[8] the organizers assembled for another, larger convention in 1973 and over 10,000 fans registered to attend. The Committee planned better in 1973, picking a larger hotel, The Commodore, and this second event was the first one that actors James Doohan and George Takei attended. Mr. Spock, aka Leonard Nimoy, made a surprise appearance - he happened to be in town - and was almost mobbed.[9] One fan has blogged about his recollections of attending the 1973 convention here.[10]

One of the highlights of the convention was the fan built life size bridge of the Starship Enterprise. In his book “Star Trek: The Complete Unauthorized History”, Robert Greenberger describes how fans disassembled the bridge, which was housed in update New York, and transported it down to Manhattan to be reassembled for the Committee conventions . Fans would photograph themselves on the bridge often wearing costumes.