Suppose I have a large home with two windows. Assume the home forms a perfect seal and does not leak fluid other than from open windows.

The window in the bottom of the home is open. The window on the top floor of the home is closed, with a fan pointed at it, blowing air at it. When I open the window in the top floor, how can I estimate how long it should take for air to flow into the bottom window?

My first thought is that the negative pressure propagates through the house at the speed of sound, at which point, upon reaching the bottom window, air begins to flow into the home, but I’m doubting this answer for some reason.