Funny, i saw the thread title and thought it was going to be about like how did the government build the initiative...without anyone noticing? Now there's a question to mull over... then whens and wheres and hows...
I've often wondered about that. too. My theory is this: We know that the Initiative was around as early as World War 2, because they "recruited" Angel at that time to rescue the American sailors on the captured German Submarine. Before the war, during the Depression, the National Reclamation Act put literally hundreds or thousands of otherwise unemployed Americans to work building things like roads, bridges, dams, AND SCHOOLS. It wouldn't have been that difficult at that time, while building the USC Sunnydale campus, to add a deep subbasement to each building in which to store "strategic materials" such as surplus military equipment which, for security reasons, wouldn't show up on any existing blueprints or campus documents. By rotating entire work crews frequently, very few people would actually know the full scope of just how large the total underground complex actually was.
Then, after the college was officially opened, it wouldn't be that hard to have, among the huge influx of returning veterans seeking further education under the G I Bill, to include at least a small group of assorted Army Corps of Engineers and Seabees, all residing at a central frat house, among the students whose actual job at the school would be to connect all of the subbasements into one huge underground complex and set up the underground facility using those "strategic materials" stored there.
Aside from the main entrance in the Initiative's frat house, there would undoubtedly be others scattered around the campus, as well as underground access to the series of caves and tunnels that apparently run underneath most, if not all, of Sunnydale (caves and tunnels that, no doubt, had been expanded by the Mayor in order to allow his vampire/demon henchmen a way to travel about town undetected).
By using those tunnels and passageways, agents of the initiative would have little trouble installing listening devices and, later TV cameras at strategic locations around town in order to keep track of demonic activity (and, knowing servicemen, probably a few in various women's locker rooms around campus as well as other non-strategic locations. Remember Walsh's video feed from Riley's room? Old pervert!)
that Andrew and his friends were able to tap into and expand later.
(Sometimes I think that I have too much time on my hands and too vivid an imagination)