In some ways the counterparts to the 1st Division, the SOG is not from our timeline, but instead from the result of an as yet unknown Time Line Split that happened at some point in the past. With the advent of time travel, and the inception of the Time Wars, humanity took a step back from space, and its efforts to expand and colonize the reaches out of Earth's orbit. While asteroid mining and other activities do still occur, the shift of focus and energy to the Time Wars was arguably part of the issue that brought the 1st Division and their entire time stream into conflict with their counterparts & the SOG.
The Warp Grenade, an invention of Dr. Darkness, that made its way into use by 1st Division, and other groups in extreme circumstances was the catalyst. The concept, of being able to concentrate a devastating nuclear blast into a adjustable small radius even down to a single room, was both enticing and frightening to behold. With the promise that all the excess radiation & energy were being shunted through a wormhole out to the vastness of space, where there would be no damage done. Unfortunately due to the still not fully understood nature of the wormhole technology, a byproduct of the theories used to design the Chronoplates and allow for time travel, this was not fully the case.
The energy was indeed being shunted out into space, where there were no inhabitants or things to be damaged in the main timeline, unfortunately they were also being shifted into the split timeline, one in which the Time Wars never came into being as they did in the original, their UN having listened to their Dr Mensinger. Instead they had focused their efforts into spreading the reach of man into the stars, which unfortunately left them with shipping lanes, and colonies, and transports that found themselves mysteriously attacked by nuclear blasts, killing thousands.
With the eventual discovery of where the attacks, even as unknowing as they were, were coming from, and the realization of the nature of their time lines situation, All efforts were put into safeguarding their existence.
Unfortunately this meant the destruction of the other timeline, and to that end, they formed the Special Operations Group (S.O.G) whose primary purpose would be to travel back in time, and cause enough damage to the timeline of the 1st Division, to ensure that their future didn't occur. This was made complicated due to the fact that the true split point was unknown, thus restricting the fields of conflict slightly. They would have to make sure that whatever split that initially allowed for their universe to come into being still occurred, but that past that point, history diverged in a way to preclude them being attacked en-masse by a similarity technologically advanced civilization.