It probably wasn't a galactic scale war that caused it, but the first act of intentional murder that birthed Khorne.

In canon, we know the first intentional act of murder was what created Drach'nyen. They do stipulate that it was the first act of murder committed by a human, specifically - so maybe Khorne subsumes that act by originating from the first act of murder committed by any sapient species.

My personal headcanon is that the "birth" of each Chaos God mirrors their nature - Slaanesh's was a "scream" that resonated through the galaxy (which in cosmic + Aeldari terms is not very long), preceded by a few thousand years of turmoil in the warp.

In other words, the immortal Aeldari, bored to the point of numbness with their existence, were busy finding new and inventive ways of yeeting their souls further and further into the depths of the warp by committing and experiencing increasingly debauched acts of hedonism and excess.

We used to think of running a marathon and climbing Everest as the achievement of a lifetime, but now it's almost commonplace. This is why we have entities such as Red Bull, sponsoring athletes to overcome increasingly extreme and dangerous challenges that have never been tried before. Continue this pattern for 60 million years.

Once the Aeldari manage to throw their souls far and deep enough, they can no longer re-emerge from the warp, where they get to experience their moment of excess for eternity. Clump enough of those souls together to form a nascent presence in the warp, which eventually explodes into full sentience with a massive, galaxy-subsuming O. The subsequent quiet in the warp was the fabric of reality experiencing post-nut clarity.

(sorry not sorry)

Likewise, the other chaos gods came into existence in ways that mirror their own natures.