Warfare is not human nature. It's the way that our culture has developed
The way our culture developed is part of human nature. It's not like it suddenly came to be what it is. Culture evolves in the same way genome does (in fact, they affect each other).
The problem with that argument is that if genome and culture develop in lockstep, then either 1) there cannot be any significant differences between cultures, or 2) there must be significant, culturally-determined genetic differences between cultures. But there clearly are differences between cultures, so it can't be 1). And humans are not genetically diverse enough for 2) to be plausible.
War is just a manifestation of parochial altruism, which is widespread in nature and is not at all unique to homo sapiens.
Let's define war as lethal group violence within a species. There are some limited examples of this in chimpanzees. Where else in nature would we find it?
The first archeological evidence of warfare is from 10,000 to 13,000 years ago, long after homo sapiens reached anatomical modernity (which was around 200,000 years ago).
The problem is that it's kinda hard to get archeological evidence of warfare when war consists of bashing each others' heads with blunt tools.
We would look for skulls that had been bashed in with blunt tools, or ribs damaged by sharp tools, in significant enough numbers that we would know that we were looking at group violence, not just one-on-one. That is what does not show up in the archaeological evidence until 10k-13k years ago.
However, we do have good reasons to believe that war long predates anatomical modernity for humans - other great apes also engage in it. Already in that time period you mention - 12,000 years ago - warfare was so widespread that we find numerous evidence of people who died from violence from other humans - up to a half of all of them.
I'd be really fascinated if you would point me to the evidence. I read the John Horgan ('End of War') book in fact-checking mode, seeing whether I could find holes in his evidence. If you have this evidence, it would indeed be a hole. Bear in mind that "violence from other humans" is not good enough. We are talking about war, not murder. It must be group violence.
The main reason why early Paleolitic didn't see much warfare in practice was of extremely low population density. When there are more lush lands to spread to, war raids don't have a good ROI, so evolution tends to favor groups that are not overly aggressive. Once we moved on from roaming hunter-gatherer societies to argiculture, warfare started to have a very high ROI (lots of stuff to loot, all in one place). Cultural attitudes towards war follow from that, not cause it.
Yes, this is possible, and an interesting argument. If we found a culture who lives in proximity to its nearest neighbor, but does not engage in war, would the argument be able to accommodate that?