He's probably referring to the rise of what we'd see as the path of the state, and technology. Cities, complex stratified social structures, laws, trade, writing, mathematics, monuments. All of these did really start about 6000 years ago or a bit more (maybe a few thousand more depending when you date it from, but it's close enough to figure the concept he's got).
But in saying that, I have to add a personal comment that this is a "something-very-narrow"-centric view in at least 2 if not 3 ways.
First because "science" isn't technology. Science is the scientific method much more than any technical manifestation. The idea and drive of trying things, seeing what works, what doesn't, building knowledge empirically, trying to find rules that fit the observations, and then refining, testing, experimenting, and improving on those rules, passing what had been learned down the generations for others to use and start from. The ancient Middle East and China didn't shoot up from nothing. They in turn built on hundreds of millennia, maybe a million or more years of humans doing science, not a mere 6000 years. Slowly (very slowly at first) and gradually. Caves and ventilation, fire, and how to use and manage it, hunting methodologies, tools, textiles (or in very ancient times, furs and tanning techniques), stone making, metal making, pottery making, safe and unsafe plants and all their uses, agricultural technologies and methods, conceptualisations... All of these from a cold standing start, and a paleontologist would walk you round a museum to show how they used science, in the form of the scientific method, which they also had to discover empirically as well. It wasn't modern (post-Pyramid!) technological science and it wasn't thought of or organised as "science" is. In that regard Newton was right. Paraphrased, we stand on the shoulders of others...... and then we think how wise we are as a result. Make no mistake just how much "real" science and "real" discovery of + through science was there, before the first ancient Egyptian ever built a pyramid, before the first Australian native ever built a floating boat or canoe.
The second way he's missing the point is the marginalisation of so much in that sentence. To judge that it's today (or in these times) that we can "really" congratulate ourselves and we "really discover" science. To eliminate in a figure of speech, half the human species from that adventure. If we stand back, we know more now that was known in the past. We will know more in the future than we know now. Science has guided us since way, way, back. More surely now, and quicker, but it has been there since the first proto-humans started to discover what made good hammer-stones and bad ones, back in the days when flint was cutting edge technology that kept us alive. It will be there in future. No generation is privileged to claim to be the epitome of science or the small period of time when "real" (rather than "fake"?) science was the norm. We will probably look like ignorant fakers in 4000 years when they look back at how few people "really" understand much of anything scientific, or think scientifically, or "do" science, if we're still around.
In short, it's clear what he's referring to. But the point being made is very weak and I would not suggest it is taken as anything like truth, without really considering what "really" science is.