Hell, at the Alyx part of the plot the human resistance are struggling to figure out what the combine are even doing on earth, all the humans are rounded up whilst giant megastructures are popping up out of nowhere, no need to explain to the humans whats really going on. Its probably the most realistic alien invasion story, since the aliens dont just politely announce their presence and intentions, they just unleash total hell on us that we cant understand until we beg them to make it stop.
The 'EARTH SURRENDERS' newspaper mentions that Breen has learned to communicate with the Combine after a long period of unexplained chaos, at that time it wasnt even called a 'war' because earth was in such a huge pile of nonsense that they didnt even fully understand they were being invaded. In just under 7 hours the combine forces destroyed earths defenses and got us to surrender. Remember that it isnt even 'just' the combine that the world is dealing with, its all the side-effects of the portal storms with alien creatures popping up EVERYWHERE, we wouldnt even know where to allocate our resources as in that short of a timeframe nobody would even know what the enemy IS, plus having any sort of coordinated government or millitary whilst every local area is dealing with its own smaller crisis would be impossible. The 7 hour war refers to the initial combine invasion, after the events of half life 1.
