Well, at least I can answer this question... November 17, 1993. Here's a link to the first ATGS post.
A little bit more for historical reference:
Don Del Grande, who responded to that first post, is a member here. That's got to make him the most veteran member of this community. There are about a dozen of us (including Chris Lemon, Zach Horan, Chris Lambert, Dave and Robair Mackey, and, of course, your benevolent dictators) who still regularly post here and have ties to ATGS going back to 1994 and 1995.
When Mr. Lambert calls his website "The Original Game Show Page", that's not idle boasting. It dates to October, 1994, back when most people still hadn't even discovered the internet.
For those of you joining the party fairly recently, it's really hard to describe what a wonderful place ATGS was for many, many years. I have many close friends that I wouldn't have if it hadn't been for ATGS bringing us together. I also know many people I consider friends that I've never even met in person, but for whom I would do favors at the drop of a hat.
As much as this forum has been successful in most meaningful ways, there was something special about the sense of community we established in those early days, when we were all just feeling our way around the new technology and simply discovering for the first time that there were people out there who knew more about game shows than we did!