It seems much more likely to just be invention of fire and control of fire. Turning cellulose into energy that promotes some sort of evolutionary advantage is pretty limited in the macroscopic biological world. Sure, cows and the like do it, but only by enlisting the aid of bacteria and having four stomachs, etc. This excess energy and exclusive ecological niche then allow for more complex social systems, feeding into some sort of positive loop selecting for intelligence.

That's all conjecture from me, but it seems to make sense from basic principles.

Well first one got idea to use bone to bash heads from mysterious black box, the rest, as they say, is history.

No, it was more likely the diffusion of technology (agriculture, writing, the wheel, and so on), not the competition between civilization, that led to humanity’s intelligence explosion.

Do you have evidence for this claim?