The players are the scum of the military, people who were too useless, dangerous or incompetent to keep around, but not worth the hassle of discharging. The entire leadership of the organisation consists of those who were too zealous, too fanatical to do their jobs, but not so incompetent it was grounds for discharge. They've been rammed into this organisation, created as an administrative black hole in a desperate attempt to clean out the scum of the armed forces of the world, given the most insane paranoid goal the world could think of to guarantee these men would never be allowed into combat, and given only those resources that are cheaper to hand over than throw away, the obsolete relics of long-past acquisitions and failed research programs.
Except then the one thing nobody ever believed could happen, did. We are attacked by aliens, and suddenly this tiny shitfunded organisation full of incompetent psychopaths and retarded psychotically-nationalistic armchair generals are the only thing standing between a military superior in every way to our own and the loss of earth and the enslavement of the human species.
The governments, now panicking, throw money at you, and you throw bodies at the aliens, spending hundreds of lives in insane and incompetent strategies to buy time that could only ever have been thought up by the zeal-over-intelligence fools in charge.
Your technology slowly improves, almost as fast as the death rates, the psychological traumas, and the horrific collateral damage, and through retrograde technological adaptation and sheer Darwinism you've turned billions of dollars and thousands of lives into a few dozen soldiers who actually stand a chance, every last one of them insane, running the gamut from acquired sociopathy to outright psychosis.