It is possible (for example) that the key innovation in the neighborhood of grain agriculture was not the creation of a food surplus - there have been human cultures with large food surpluses since the invention of the fishing net and the tended orchard . . . .
Grains were not the first cultivated plants. The oldest evidence of agriculture (unnaturally hybridized species or varieties) is fig trees in the Old World ca. 12KYA and pepper plants in the New a couple of millennia later. The tended orchard was indeed the first Neolithic technology, although without domesticated meat animals they still had to do a lot of hunting. One reason for the relatively late timelines of the paradigm shifts to permanent villages and then to cities in Mesoamerica was, in fact, the complete absence of large herbivores to domesticate for food and traction. The largest domesticated animal was the turkey and the only animal that could barely be used for traction was a dog dragging a travois. I have often expressed my wonder at the determination of the Olmecs (or whoever came first), who built their cities without the help of donkeys, oxen, goats, horses, etc.
As for fishing, there is indeed evidence of permanent villages established on the shores of rivers and seacoasts, where fishing was abundant. Some of these communities experimented with farming, although they had no reason to invent animal husbandry. These communities were certainly
Neolithic culturally, even though they don't quite satisfy the textbook definition of the word. However, there's no evidence that any of them made the next Paradigm Shifting transition from villages to cities. I haven't come across a good discussion of this, but my guess is that since there's a limit on the number of fish that can be taken from a single location, this put a limit on the size of the villages. Inviting another tribe to join them and enlarge the population would be disastrous, whereas in a true Neolithic village with both farming
and animal husbandry, increasing the population resulted in greater prosperity due to division of labor and economies of scale.
. . . . but the ability to store it for more than a year, to ride out a supply failure.
Storing food was very difficult with Paleolithic technology. The invention of the technology of
pottery in the Neolithic Era was the first step toward solving that problem. There was no reason that Paleolithic people could not have discovered the technique earlier (and perhaps they did and used it for ornamentation, although I haven't seen any articles about that), but since pottery is heavy, bulky and fragile, it would be of little use to nomads with neither wheeled vehicles nor domesticated herbivores to pull them.
Grains keep. But grains are not good food, in general, and the people who relied on them early were not robust and healthy, so whether the populations of grain-eaters boomed in consequence of (presumably) not busting in bad years is not really known.
As I've noted in other threads, in the late Paleolithic Era the life expectancy of an adult who had managed to survive childhood was in the low 50s. Fast forward 15,000 years to the Roman Empire. Huge populations needed massive food supplies, which required vast swaths of land devoted to agriculture. Furthermore, the agricultural land had to be outside the city where land prices were cheaper. With only draft animals as a power source, food had to be very sloooowly carted in from those areas. Now meat doesn't keep well (in an era before the invention of refrigeration), and furthermore pasture for meat animals is a very inefficient use of farmland. (Dairy cattle are ten times more efficient as a source of food than beef cattle, but milk spoils even faster than meat.)
As a result, only the aristocrats had a significant ration of meat in their diet. The peasants and slaves had to get by on bread, baked in the city from wheat (with its long shelf life) grown in the countryside, plus a bit of cheese, eggs, nuts and/or seeds that barely gave their diet a proper balance of amino acids. These people did not understand vitamins and minerals. So the life expectancy of the average peasant in the glory days of the Roman Empire was about
23 years!
Meanwhile there has been one major planetary bust that we know of, coincident with and often blamed on a large explosive sulphur volcano in Indonesia a few tens of thousands of years ago . . . .
Is that what caused the dieback and near extinction of
Homo sapiens while our ancestors were all still in Africa? Do you have a more precise date?