The Red Ocean was the current focus of human civilization. The Big Two were the major pushers of the invasion of the dwarf galaxy.
In fact, despite the arrival of billions of humans through the beyonder gate every day, the expansion effort was still led by the Mech Trade Association and the Common Fleet Alliance.
The resources they monopolized and the tech they had mastered for a long time served as the basis of their unstoppable progress in the frontlines of the expansionary war.
No alien civilization could possibly hope to match the might of the Big Two's battleships and mechs.
Under the unceasing advance of humanity's greatest war machines, entire alien fleets rent asunder and whole developed planets were scoured of life.
The huge power disparity between a top power in the Milky Way and the local powers of the Red Ocean meant that the former did not have to play nice with the latter!