one of the earliest Star Trek conventions occurred in 1976 at the Northgenn Mall in Denver Colorado in Fall of 1976.
Only 7 years after the series ended, Star Trek already had a very strong cult following in the US and even abroad. There were small fan clubs popping up all over the world, so after a while it had such momentum that someone began organizing these gatherings into conventions...
At homes, schools, malls, they eventually had to rent large convention halls to accommodate the throngs of devoted 'trekkies'.