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Consider the sheer volume of people you need to create, say, a viable rocket to reach the moon and return. Several different kinds of engineer to create the circuits and fuel and engine and craft, right? Support staff. Miners to mine coal and ore, refiners and smelters to make steel for parts and silicon for chips, drillers for oil and refiners for the fuel, construction workers to build their homes and the launch pads and everything else, farmers to grow food to feed all the miners/drillers/refiners/construction workers/support staff/engineers. Doctors to care for all of the above. Et cetera- what about entertainment? Other desires? Is reaching the moon the sole telos of this civilization, and every job aimed at that goal? If not, the scale balloons as people take other jobs towards other goals. And I've left off huge numbers of other factors and 'needs.' Some could be left out or leapfrogged, but not easily.
An industrial civilization is a massive pyramid. One can imagine an ideal civilization perfectly following a tech tree with no deviations and no waste at a smaller population number, but one can imagine six impossible things before breakfast.
There's some Greater Variability there too. Written language only developed independently a few times, so think of Sequoyah- once the idea was demonstrated he sat down and spent years developing the Cherokee syllabary. He had the ability to create written language, but not the spark. In the thousand years before him, how many of his people had the ability and not the spark, and how many lacked even the ability? A bigger population gives you more rolls of the dice to generate people who even have the possibility of doing new things.
Or look at the Congo and Empire of Dust. Or Google Maps of certain parts of Johannesburg 10 years ago versus today. Or Detroit, 1950 versus today (though in some ways it's recovered from rock bottom). Without the right kind of support, the right sort of culture, an industrial civilization decays quite rapidly, and maintaining that requires a lot of people.
I am not sure that a society that can't do "moon mining" isn't an industrial society (...is Earth not industrialized today?) but I am not convinced doing that needs a large amount of people, either. Your minimum viable orbital rocket company (RocketLab) has less than 3,000 employees, a third of a percent of a million-person society. My assumption is that expertise is relatively resource-cheap - after a certain small point, more people are mostly doing things faster, not qualitatively differently.
As regards the supply chain: chip fabs don't need to be big, Polar Semiconductor is operating with staff in the hundreds (likely). Smallest viable mining, farming, and construction operation is a single guy, so that scales very efficiently. USA Rare Earth has less than 200 employees, so it's possible to do refining at a very small level. Doctors are not a high-density need, and neither is entertainment.
I probably should have stipulated that I wasn't imagining a society built from the neolithic on up from scratch, although that's interesting too. More like "how few people could we export to a remote Pacific Island and have them run a vertically integrated industrial society." I think all of your concerns about "how would we produce an Einstein on a seven-digit population" are all worthy objections, but I am more interested in "now that we have Einstein and all the other guys, how far could we slide without losing that."
Realistically, I think the answer varies tremendously based on the population's demographic pyramid. But with a healthy or at least not inverted population pyramid I am not convinced the number is very large.
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