Note that this is a different canon from the previous 1984 and 1989 films. That version Firehouse is covered here.
The Firehouse was a location considered for a headquarters in the 2016 movie. It eventually became their headquarters after saving the city from Rowan.
As the women were looking for a new place for operations by means of a Rental Agent, she introduced them to the Firehouse. However, after Erin asked about monthly rent, which turned out to be $21,000 a month, they ended up picking a much more budget friendly location.
After saving the city from Rowan, the Ghostbusters were finally able to, with government funding, move from the Chinese Restaurant into the Firehouse. Once settled in, they quickly began setting up a lab.