The miltary aspect of this race was nuked, the rest exploded. What's left isn't going to want to wage a war since they are now left without their resource extraction technology, they're weak and defenceless too, why pick a fight?
The death toll is likely to be in excess of well over a billion, nearly every major human city was destroyed utterly at once, the most populated ones had people gathering to each ground zero.
There's no money, no food, no water, no homes. Governments can't do anything to restore order as the military is gone, and no one is any more important than any other now.
I mean hell America now everyone shoots anyone in their way, imagine the world left after the aliens, government mowing down anyone who doesn't obey, citizens exerting their right to any left over resources etc
Moonbases and starships just a few years after that? alien invasions and Apple devices accomplishing something useful is worlds more believable than that.
Well, the entire movie was unrealistic (to put it mildly) but even in our urban era you can't discount the rural areas.
In fact, without them the cities would die in a matter of days. The aliens concentrated on the larger cities like capitals of the most important nations and other areas like Los Angeles so they are pretty much gone for now.
However all the farms, cattle herds and such are outside of the cities and i doubt the aliens had enough time to attack them too so they would be pretty much intact. I'd also theorize that the infrastructure up to the cities is more or less intact too.
What this would mean is that after the first chaos dies down (give it 1-3 years) humanity will reorganize, new leaders will step up (especially the US president who must be a world known hero now having led the crucial strike himself) and as one of the central themes of the movie states humanity has united as one race and is pulling in one direction now.
Once again.. the movie is a total fantasy but if we keep in that area i don't find it unfeasible that humans could build a base on the moon in the 20 years after the attack.
What is preventing us from going to the moon or Mars today? Costs.. it's just too expensive for pure research, government funded space trips. We could do it easily if we didn't care about the costs and would use a fraction of the world's military spending.
Now throw in alien interstellar technology and landing on the moon should be a cakewalk. Who know what else this technology could improve?
Given that humanity now knows it's not alone in this universe and that at least one alien race is very hostile i can fully believe that we would get our asses in gear and went frantically to work reverse engineering the tech and putting it to good use.
Just look at the Middle East, especially Dubai, and what they accomplished in 20 years when money is not an issue and enhance this with alien technology possibilities and you have got ID: Resurgence.