Yes, and not just for food and similar non-human resources. Reducing competition for mates is a common reason; even well past hunter-gatherer society, killing the men to take the women as mates remained a thing.

E.g. the Comanches had a longstanding war* with the Apaches not because they wanted to seize each other's grain stores, but rather because they wanted control of the best buffalo hunting grounds.

* Not a war in the sense that we'd call it today. There were e.g. no organized charges, battle lines etc. Maybe "long slow series of irregular cavalry skirmishes" is more accurate than "war."

Minor motivations and proximity are enough to set it off. And thereare plenty of motivations anyway: fighting over good hunting areas, water, gathering areas, and women.

Keeley says peaceful societies are an exception. About 90-95% of known societies engage in war. Those that did not are almost universally either isolated nomadic groups (for whom flight is an option), groups of defeated refugees, or small enclaves under the protection of a larger modern state. The attrition rate of numerous close-quarter clashes, which characterize warfare in tribal warrior society, produces casualty rates of up to 60%, compared to 1% of the combatants as is typical in modern warfare.