> It would obviously be possible, since we have CPUs now but once lived in caves.
That's a big assumption. The modern world was built in easily accessible fossil fuels. We've used basically all of the easily accessible oil and a lot of the easily accessible coal.
Without an easily accessible surplus it's hard to go from agriculture to modern society.
We also dug out millions of tons of useful materials out of ground, purified them and concentrated them in cities and along roads etc. We cleared forests on most of continents to let people do farming there.
In Eastern Europe at least the biggest limit on farming and state-building in early middle ages was clearing the forest for farming. It was the biggest energy expanditure for people there, and it took hundreds of years to get to a state in which most of the land is available for agriculture. If the apocalypse was quickly over - we'd get to continue from that point without spending all that energy again. If it takes 50 years or more - most of Europe would be one huge forest again.
Depending on the kind of apocalypse all you'd need to do might just be to scavange for usable solar panels/wind turbines/car batteries and starting agriculture in the places that are still available.
Or you'd need to start from scratch, but then we're talking centuries.
Impossible, you wouldn't have any of what's needed to build a solar panel. No rare earth, no plastics, &c. they're all byproducts of the virtually free fossil fuel we had at the begging of the industrial revolution. You could find oil oozing out of the ground in some places
We probably wouldn't even be able to source iron ore at that stage, let alone process it to make any kind of useful turbine, but let's say you make a working steam turbine from wood and clay, a DIY solar powered steam turbine is quite a few steps before modern CPU
Depending on your location, there are places where you can't not find iron. Recycle! Civilization might be lost but all that processed and purified iron didn't disappear, it's just hiding under some dirt.
That's a big assumption. The modern world was built in easily accessible fossil fuels. We've used basically all of the easily accessible oil and a lot of the easily accessible coal.
Without an easily accessible surplus it's hard to go from agriculture to modern society.