This is a 1952 Poul Anderson post-nuclesr apocalypse novel.
There are two major categories of such stories: recovery will be painful, but human spirit and knowledge of how to rebuild is widely enough known to do so; a new Dark Age will result from ignorance of survivors.
Vault of the Ages is sort of in the middle. Five hundred years of Bronze Age culture with some use of salvaged steel and copper from the still feared cities. But eventually someone not terrified of the taboos of the memories of radiation poisoning gets into a vault of knowledge about science, technology, and the humanities and restarts. (Humanities were still of merit in 1952.)
I generally land on the optimistic side. Almost everyone is know has enough understanding of tools, machine tools, and the guts of industrial civilization that rebuilding would be painful but not hopeless. We do not need to reinvent machine tools, assembly lines, light bulbs, electronics. The knowledge is either widely distributed or in books.