The current Government Center bunker, um, T stop went up in the early 1960s as part of the transformation of Scollay Square into Government Center.
In the photo above, from Boston City Archives' Government Center photo set, note the parking lot where Center Plaza would go across Cambridge Street. In this view, you'll see the answer to the chicken-egg question of which came first, the subway station or City Hall. Below, that's the low part of the JFK federal building still under construction:
Compare that photo with this MBTA rendering of what the new Government Center station will look like in two years:
H/t John McLachlan.