Not that long ago, when we were talking about the "best case scenario" for Christianity, I wrote up
an outline for my interpretation of that idea. That ATL scenario would also double quite effectively as a decent stab at answering this challenge here. (Interestingly, my starting point is quite similar to what
@ATP argues, above, and I think we're envisioning a reasonably similar sort of outcome. Although I wouldn't expect a scientific revolution
that early. It conservatively estimate scientific and technological progress to end up one ot two centuries "ahead of schedule", compared to OTL.)
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Of course, earlier PODs than such a one in Late Antiquity can be imagined. We can go further back. One issue is that the further back you go, the hazier the outcomes tend to become. You really have to "steer" events to produce the outcome you desire. At that point, it's more "world-building" than real "speculation on a counterfactual scenario". Not that this necessarily deters me. I have a long-cherished idea for a scenario where
everything goes right for Alexander the Great, and he ends up founding an empire that lasts a thousand years. This is completely unrealistic, but it's still very interesting.
That particular scenario has Alexander funding Aristotle's philosophical school after the old master's death, and ultimately establishing an organised system of proto-universities throughout his empire. (Essentially combining such institutes as the Lykeion, the Gymnasion, the Mouseion and the Serapeion. At the same time, all the great libraries within the empire are diligently copied, so that duplicates of all known works are present in the great imperial libraries of all imperial cities.)
The fact that Alexander's dynasty is viewed as divinely ordained, and their emblem is the blazing sun, also ends up helping the
very early acceptance of the heliocentric model along...
Long story short: by the time we reach what would in OTL be called the 7th century, science and technology are roughly equivalent to what we had in the early 1900s in OTL. Roughly 1250 to 1300 years "ahead of schedule", give or take. But of course, this is hardly the most likely scenario, and it's very much a "steered timeline" that's intended to produce certain results.
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If you
really want to go crazy with this, we can go towards the truly speculative, and imagine what the world might look like if the
Younger Dryas never occurred.
Note that agriculture was invented by different societies across the world, at roughly the same time: namely soon as the global climate allowed for it. This began roughly 10.000 BC, with the first semi-sedentary societies being recorded around as of 9500 BC. However, the world first moved out of the glacial period around 13.000 BC, reaching the kind of balmy climate that modern man enjoys around 12.500 BC already! And then things fluctuated a bit in the Bølling–Allerød period, but the overall global climate was warmer -- and, we may infer, more hospitable to sedentary ventures.
But then... the Younger Dryas. First a massive meltwater pulse, then a millennium of returned glaciation, and then another and even greater (and faster!) meltwater pulse.
I actually suspect that humans really do tend to invent agriculture as soon as circumstance allows for it and sufficiently motivates them to do it. I wouldn't be surprised
at all if there
was a first, abortive Neolithic Revolution in 13.000 BC, first producing results in 12.500 BC or so... only to get totally screwed over by the Younger Dryas, which meant that humanity had to largely repeat the whole process afterwards. (This means that the concept of an "ancient, antedeluvian society" may actually have some merit. No crystal spires and togas, though. In fact, they'd still be in the stone age. But look at
Göbekli Tepe, and imagine something like that... but 3000 years more ancient still!)
Now suppose that the Younger Dryas never happened. The melting of the great glaciers is a far more gradual process -- slow enough for humans to adapt, to very gradually move a bit more inland as the sea encroaches over many generations. And there's never a thousand-year winter. In that secenario, we may posit, the tentative developments that we saw emerge around OTL 9500 BC could instead commence as early as 12.500 BC -- and be sustained thereafter!
In other words: we don't lose three thousand years to the vagaries of fate. Instead of something like Sumer arising around 5500 BC, we might expect the first emergence of "civilisation" around 8500 BC. Assuming a roughly similar pace of innovation, by the time that the Iron Age got going in OTL, the denizens of this proposed ATL may be watching the first moon landing.
