The country is in a Cold War. Let’s say you, a government military official, wants to create a biological super weapon away from the prying eyes of those who think humans have natural rights. My question is, could the military plausibly create an entire town, for the creation of a super weapon, without their secret getting out?
Yes. That actually happened.
The US government built entire towns when developing the atom bomb. See these references for more:
Yes, it's just a matter of how much effort the government is willing to make.
The Soviet Union had many secret research cities.
These were denominated as secret cities, places where the most advanced industries developed and they did not appear on the map of the USSR, because they wanted to hide from the world and the American enemy the military and technological advancements of the nation.
In response to the immense challenge of the unfolding East-West arms race, Stalin decided to create dozens of centers of research and development excellence in the USSR. Some of these so-called "Naukograds" [Science Towns] were "Akademgorodok" [Academic Cities} devoted to basic research. Others were secret cities which were to provide the technical foundation for Soviet military technology - sputniks, long-range missiles, thermonuclear warheads of extreme yield. Among the work performed in such places were chemical, biological and nuclear weapons research and manufacturing, enrichment of plutonium, space research, and military intelligence work.
So, if your setting is similar to the modern age, what would the government have to do to keep the city secret?
Who is the government trying to keep the city secret from? Other governments, or just the public at large?
Here are some ideas:
Build a fake factory town around a fake mine entrance, which disguise the transport links and support facilities.
Then build the secret city deep under the mountain range the fake mine entrance opens into. Like, with this thing:
Don't put the city on maps, in the postal system, in the phone directory, or anything like that. Have all connections go through a covert facility disguised as a shipping company or a big warehouse facility, which then forwards supplies, mail and telecom to the fake factory town.
Swear everyone who works there to secrecy, and don't let them leave for a number of years.
Have a fake front private security company patrol the area with troops who are really government soldiers in disguise, to detect and stop anyone coming near.
Ok. Let's try to do this.
Since you can't just start in a cornfield, or patch of desert, you need a cover:
Everything you do is going to photographed from a satellite every two weeks at minimum. So you have to do everything in a way that is 'analyst resistant'
So build your city in Detroit. Detroit was dying a few years ago.
Buy up the places that are still in use. Demolish many buildings. Build underground. Carry out a desultory economic recovery to mask the change.
So build your city in an abandoned town. Uranium City was abandoned and went from a town of 5000 to a town of 500 in 3 weeks, and to 50 in a year when the mine shut down.
So officially close a military base. Or don't close it, and just trade one set of secrets for another.
Have a world's fair. When it closes, it becomes the town.
Take over a destroyed refinery. Rebuild it to look like a refinery, but inside tall towers do your secret work. You can't see oil being pumped in pipes.
Ok. That takes care of the satellite stuff.
You need to mask the activity too. No one will believe part of Detroit is abandoned if there are 50,000 people arriving and departing in rush hours. So you build a subway that handles freight as well as people. Disguise THAT as flood control.