That's an interesting thought. ACOUP did a blog post a while back [1] outlining the very specific circumstances that led to the Industrial Revolution and arguing that it's hard to imagine another way it could have happened. I suppose a rebuild would have to find a completely new route. Perhaps fields of Don Quixote esque wind mills connected to giant led-acid batteries rather than coal! With a couple hundred years gap between Armageddon and a substantial human population making progress, at least there would hopefully be decent timber reserves to work through the early phases.

[1] https://acoup.blog/2022/08/26/collections-why-no-roman-indus...

I think the level of scientific knowledge we have accumulated would be a tremendous short cut.

Even without books, the myths and obvious ruins of previous technological success would be a huge cultural guidepost for recovery.

Perhaps we would go through a 1000 year energy poor "dark age", and recovered populations wouldn't peak as high as ours, but I would expect that to be the worst case if an awareness of our history was not lost.

And maybe 10,000 years, after a complete cultural breakdown to hunter gathering with little functional memory of the past.

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Given rewrites of first versions are often much improved for having seen previous failure modes, it would be interesting to pop into the future of a recreated civilization and see how they might do things better!

If you can jump right to electric power, then hydro power can give you all the power you need to get civilization going again. I don't think that tech knowledge would be likely lost if people survive at all.

I guess it depends on how long before the collapse happens, but I think there's enough accessible fossil fuels left to sustain a less than 10-figure human population for under a century while it figures out what else to do. They'd probably have to live with far more local supply and distribution networks, but global communication should still be fine.