The Nostromo was constructed in 2101 as an interstellar cruiser, but was refitted in 2116 as a commercial towing vehicle. The ship was subsequently operated as a commercial hauler, transporting automated ore and oil refineries between outer colonies and Earth.
It set down on LV-426 on June 3, 2122
-Aliens: Colonial Marines Technical Manual, p. 135
As it was returning to Earth when the events of Alien went down and we know it was refitted in 2116 (presumably on Earth) that would give a final launch date anywhere between 2116 and 2122.
A:C took place in 2104
18 years before Alien
12 years before the earliest date the Nostromo could have left Earth.