But if UFO took place in 1980 (the year that flashes onscreen in UFO's opening credits, multiple times), and the two series are in the same fictional universe; Mooonbase Alpha was probably already being expanded prior to the war.
But the the timelines don't work out if you go by the series bible and what's on screen.
The series bible says about Alpha and its personnel - 'The personnel of Moon Base Alpha consists of approximately 300 men and women, specialists in their field, who have signed on for an 18 month tour of duty', furthermore, the bible also says that there have been eight commaders since Moon Base Alpha became operational. John Koeing is the ninth, replacing Gorski on 9th September 1999.
If each commander serves for 18 months; than 8 commanders x 18 months = 144 months.
144 months divided by 12 months in a year = 12 years.
1999 minus 12 years = 1987 +/-
It should also be pointed out that Gorski doesn't get to complete his full rotation as base commander. He's recalled to Earth because he's unable to deal with the Meta Probe crisis. How far into his rotation is up for debate, is it at the beginning, middle or end of his time on the moon.
Having said all of that - it is possible that there was a base on the moon prior to 1987.
Voyager's Return says that an entire base with 200 people was lost when Voyager Two's Queller Drive kicked in prematurely and exploded.
The draft script says that this was another Moon Base (although that line was deleted/not mentioned in the final episode).
So, what if it the UFO Moon Base that was destroyed by Voyager Two and Moon Base Alpha is the replacement, being built after the war of '87.