The Native Americans of the Olympic Peninsula produced a complex civilization without agriculture of any kind.

That was made possible mostly by the unique weather and ecology of the area; it can't be done in most places, but it can be done in enough places to keep humanity from going extinct.

There is a vast range of non-native eadible plants and animals that have now been introduced to every country.

That would make a huge difference compared with traditional indigenous societies. However farming does require steady state weather - which is unlikely after a nuclear war?

There still isn't enough to sustain people on subsistence farming. And subsistence farming, is well, subsistence-level - it precludes specialization which means it precludes most of the advantages technology brings us today.

If you're ever in a civilizational collapse scenario, literally the most important thing you can do is rapidly restart the farm supply chain by whatever means necessary - anyone imagining building a fortress for themselves is building a tomb.

Subsistance farming for a limited number of people can be done by burying potatoes in the ground and digging them back up in the autumn. Well, it's a bit more to get a good yield, but not that much more, you can (and some places do) teach that to literal kindergartners in a single day. We can't sustain 7 billion of people this way, but if some catastrophe kills 99% of humanity, the availability of better cultivars makes subsistence farming for the remainder much easier than five hundred years ago.

Subsistance farming based on potatoes is not without its risks:

https://en.wikipedia.org/wiki/Great_Famine_(Ireland)

There are about 100 uncontacted tribes thought to remain.

Does a surviving civilization need/want to rely on the same processes that (may) have led to their outcome?