I feel like you’re going to say the invention is “human civilization.”
How well did they do? 300(ish) years and a thousand miles of western South America? Conquered by what…200 Spaniards?
I agree that writing needs language as a pre-requisite. But I tend to lean with those who see language as an evolved characteristic of human beings rather than something human beings invented.
Prior to the arrival of the conquistadors, with their guns, horses, and armor, they were doing pretty well.
And, it’s a means of communication. Animals have numerous means of communication.
Maybe it’ll be tool use.
Which I also tend to see as an evolved characteristic of human beings rather than a human invention.
The wheel and the lever would fall into the same category.
I would put fire as well as it allows us to transform material. Clay becomes ceramics. Sand becomes glass. Iron ore becomes iron ingots becomes steel.
Way, way, way better than isolated tribes stuck in caves with their campfires. 
IMO, cultivation/agriculture is by far the most critical human invention towards civilization.
Civilization as a word has the opposite meaning of what @Stoid is using it as.
The meaning “civilized condition, state of being reclaimed from the rudeness of savage life” is recorded by 1772, probably from French civilisation, serving as an opposite to barbarity and a distinct word from civility, as if from civilize.
The sense of “a particular human society in a civilized condition, considered as a whole over time,” is from 1857. Related: Civilizational.
The term, to everybody but anthropologists and their ilk, is part of a progression, from animal societies to “savage” human societies to “non-savage” human societies. The people who developed and spread the term meant specifically cities as opposed to nomadic life. Cities were themselves equated with agriculture until recently, when closer study revealed what could be called cities being founded by various other purposes. Like the evolution of humanity itself, the line of progress has been replaced by a bush of branching growths.
SO, two things. The separation of humans from animals and the growth of what we term cities.
If we go back far enough, I’d guess that the unassuming thing that separated humans was the upright stance. Other animals can walk upright on hind legs and use the forelegs for short periods of time, but humans are unique in making it a lifetime posture. That appears to have given them advantages that would otherwise have doomed them, given their lack of claws and thick hides. Large brains came much later than erectness, and we don’t really know how large they had to be to make the big difference.
If agriculture is tossed out as a progenitor to cities, I’d put defenses as the turning point. Weapons surely preceded defensive walls but they necessitated a nomadic society. Staying in one place without defenses would attract enemies, both animal and human. Long-term permanent communities required protection for, again, otherwise defenseless beings. I’m not aware of any early cities, based on agriculture or not, that didn’t have some sort of walls, earth, mud, stone, whatever was technological feasible. Long-term survival led to everything else that we associate today with a “civilization.”
Slavery was likely a prerequisite to civilization
How about the ability to make a splint for a broken leg? Before we started doing that, legs would heal poorly causing gangrene, or the person injured wouldn’t live long enough for it to heal before getting torn apart by a predator.
But once we started taking care of each other, we could have a civilization.
HoneyBadgerDC has proposed that control of water resources is basic to all civilizations. I agree with that. Poverty Point LA is an excellent example of a hunter gatherer society with major water control facilities. However if you draw the dividing line as between humans and plants/animals, their are numerous examples of plants and animals controlling water for their benefit. The same is true of farming. Both plants and animals cultivate others for their benefit.
Civilization predates writing though perhaps not art. But it does not predate the boiling of water, Somewhere in there with the control and use of fire and water you get civilization. We could nit pik the point.
So, enlighten us - what’s your take?
Sure, but cuneiform on clay tablets did that job prior to paper or papyrus. It’s the idea that you can record information like that which is the important part. And further back, being able to use language to communicate and think that enables all of the above.
I don’t know… I think that it’s really blurry on stuff like that. Did we discover, or invent the wheel? Probably depends on whether Og the caveman saw a tree trunk roll around after he kicked it or if he thought it up on his own. And really, in light of that, isn’t it the axle that’s the key part?
Cordage.
Nah, even with global warming, we’re still a distant second to cyanobacteria.
I think the difference between something being an invention, as opposed to an evolved trait, is that its something humans will always develop, regardless of outside influences. Isolate a hundred babies on an island with no other human contact (while somehow preventing them from all dying) and they’ll develop their own language. They might figure out fire, or the wheel, or whatever, but they will figure out a way to communicate with each other.
That puts it pretty firmly in the “evolved characteristic” category, not the “invention” category.
That is a question that mathematicians spend a lot of time on. Did exact categories exist before I invented them? Of course they did. What I did was reify (make a thing of) them.
Getting back to the OP, before agriculture there was no society. With agriculture, society developed. My first answer was language, particularly recursive language with subordinate clauses. For all animals appear to have language-like capability, there seems to be no evidence for a recursive language, a sentence like: “This is the whale that ate the shark that ate the bear that ate the wolf that at the dog that ate the cat that ate the rat that ate the mouse that ate the mosquito that ate the malaria parasite that infected the child that ate the date that ate the date bug.”
Is a tribe of hunter-gatherers not a society?
That’s my vote, too. Although,
Or evolve it, or a combination of all three. The development of language had to be a parallel process of both our brains evolving to be able to use it, and us learning how to use it.
But if language as a whole is disqualified, I’d say writing is a solid second place.