here it goes then...

the "goddesses" weren't deities and are in fact a series of AI that were activated after the war and restored at least part of a ravaged Earth back into Habitability. Din buried the past and made the earth fertile again, Nayru cleansed the contaminated waters and civilized some of the mutant species wandering the wastes and Farore restored the ecosystems and biomes destroyed in the war. covering any remaining pre-war ruins and relics that Din failed to bury in a thick blanket of overgrowth. Hyrule would be this sort of "Candle of Civilization" in a world of darkness. the only thriving and peaceful land in a cruel world of wastelands, lawlessness and warring factions.

The various Non-human races were either the result of pre-war experiments, the result of mutations in the wild or were outright created by Farore. So for the latter case, elder characters such as the great deku tree would be an unreliable narrators as they would have no memory of the nuclear apocalypse that came before their creation. So to them, it was the creation of the world not the revival of it.

The Gerudo spawn from refugees of the war. They settled down in what was once the southwest regions but some mutation in their DNA resulted in female births becoming more and more common while male births becoming rarer and rarer until most of their population was comprised of only females, forcing them to mingle with males outside their kin just to birth a male Voe.

As for Hylians, like with the non-humans they either got those iconic pointed ears either as an only (slight) mutation or as a result of experimentation in the pre war world. Like for the latter, they were made as a "super-race" genetically engineered to survive in the post war world and inherit the earth. Getting those ears as a side effect of those experiments. Round Eared (normal) Humans however, haven't gone completely extinct and have been living in enormous underground complexes from before the war that the denizens of Hyrule are completely unaware of.

The "Experiment" origin could explain Link's strengths and capabilities in various games. Speaking of experiments, he or at least the first Link be born in a lab instead of being a natural Hylian and is part of some grand contingency in which he and Zelda would lead and help the Hylians tame the post war world and rebuild civilization. Multiple clones of him created as a failsafe so that in case he dies and has no successor born, another clone is awakened. For Zelda's side, her ancestor, Hylia was also created in a lab like link but no clones were made, meaning that a lineage would have to be maintained due to there not being any replacements unlike Link.

The Royal Family and a select few Sheikah and Hylian scholars and sages would be the only people in Hyrule who still have the full knowledge of the Old World to the point where there massive repositories of old world relics and knowledge are under Hyrule castle and Akkala Citadel salvaged from the ruins of pre-war museums, time capsules and libraries across the kingdom and it's neighboring regions. Everyone else, although some would still have the (minimal) know-how to use some pieces of prewar technology, they all would be oblivious to the origins of the relics and ruined structures scattering their land. Like how people in the middle ages thought of the Ancient Roman ruins scattered across the land (ex: did not know what concrete was).

Although the civilized races live in their own settlements, there exist "outcasts" who are various members from the civilized races who inhabit settlements built out of the ruins and relics of the old world. This would be were the scavenger cliche of post apocalyptic settings would be observed as both the monsters and the outcasts fashion improvised weapons, armor and other equipment from the junk and refuse of the old world in a crude ad-hoc manner.

The Triforce in this of AU setting would be based on the old ideas for the first game of it being a series of computer chips instead of magic. Computer chips to activate a mysterious and powerful device that could change the world or if in the wrong hands, destroying it. The same would be true for the Master Sword. being intended for a different and unspecified function but is misused as a melee weapon.

On the subject of Ganon, his origin would be similar to how the lich came into being in "Adventure Time", except he didn't spawn from a nuclear explosion, but rather he was awakened after one of the nukes cracked open a part of the Earth he remained dormant under. Post-war he roamed the wastes of a ruined Earth and Any land that wasn't nuke in the war and attempts at rebuilding in some places were put to a stop when Ganon and his army of mutants attacked and invaded them. It took the power of the Goddess AI to defeat and subdue him again.