The answer is yes. War predates humans. A lot of things predate humans. Art predates humans. That includes art produced some 500,000 years ago, by Homo erectus.
Is there earlier art? How about bower birds, who have been making art for 50 million years?
How about language? Slavery? Domestication of animals? War? Ants did all that and more 90 million years ago.
I know ants had war, and, unlike humans, who send their young men, ants send their old ladies. But bees have war? I know bees will raid other nests for honey. But bees have wars. Certain kinds of bees. Stingless bees.
Well, why war? The usual explanation is resource scarcity. Bees need honey or pollen, or a good hive, and if the rewards outweigh the costs, why not? I think you have to throw in euscociality as well.
In which case, I would argue humans are eusocial. We have cooperative brood care, we have overlapping generations within a hive, we have a division of labor. We are a heck of a lot more cooperative and in-group friendly than our nearest relatives, the chimps.
What about termites? They go back a good 200 million years. Do they have war? They do not. Not war between termites. And why should they? Wood, dung, detritus, all are in plenty abundance. There is no resource scarcity. And yet termites have soldiers. Ah, well, because of ants.
Termites do one better than ants, but still come up even with humans.
Termites have suicide bombers.