knowledge is the key. Even Ancient Greeks could have built a wind electricity generator if they knew how - ie. if they knew about copper wire and electrical charge movement in it. And you can collect sun light and focus it on a boiler while still being in Ancient Greeks situation - that gives you https://en.wikipedia.org/wiki/Aeolipile which can be used to generate electricity too. And they could have possibly have that too https://en.wikipedia.org/wiki/Voltaic_pile or even https://en.wikipedia.org/wiki/Crystal_detector#Cat_whisker_d... - piece of crystal and a wire making a diode - and you can have primitive radio.
So, the newly built civilization bypassing fossil fuels would even be better :)
Did they have the level of materials science to build a practical one? They weren't able to produce steel, for example.
For some minerals (e.g. metals) that might possible even be a bonus, as we've brought it up to the surface and it might be more accessible than before (a scrapyard that's buried under some soil could be an excellent place to mine iron), but there won't be shallow coal or shallow oil that a second industrialization could use as a cheap power source.
We may be able to start low scale stuff to bootstrap renewables, but if we lose our knowledge, things get much harder.
I feel like this is the more important of the two points you made.
Even without Uranium, it's conceivable to have a second industrial revolution. We don't need nuclear power for that.
But without easily accessible fossil fuels, it's much harder to envision the next civilization having an industrial revolution. They might indeed never rise to our level of technology again.