How about this. Men hunt, women gather. This requires a nomadic lifestyle because game and stuff gathered begins to run out after a passage of time. So you have to move several days walk away.
But a good place to live will be close to a water supply and for the most part good places will always be good places. So in the course of a lifetime, the same place might be be used several times by the group.
When camp is set up people will use one spot or spots as a common toilet and garbage dump. Some clever person will remember that where the toilet was the last time the camp was there, there’s a lot of food to be gathered, since many seeds pass through the digestive system untouched. The next step, actually planting seeds and hanging around long enough to see them produce food is a big one.
Although agriculture and animal husbandry are more labor-intensive, they do produce a much bigger food supply, which allows for a larger human population in one area than hunting gathering. And of course there’s beer.
This happened after a hunt where several were injured. While the rest went on a small group was left to recover or die.
When they got back they found they had not only lived but thrived. They got in the habit of leaving the older people, young children, the injured and pregnant women there in a "winter camp" while the rest went and hunted.
This would have allowed the old to teach the young tool making and allowed greater time for experimentation.
They might have even come back a couple of times during hunting season to drop off dried meat, untanned hides and other raw materials to be processed. They could also pick up new weapons that were now being made with greater care and precision.
Some of the people that stayed decided to move some berry bushes closer to where they were living so as to harvest them more easily.
From there the ideas grew as bushes, trees and then tubers were moved and planted. I think that grain and veggies were probably the last things cultivated.
So you ended up with the best of all worlds. That would have lasted until people began to raise animals. But in most cultures outside of cities you still had hunters who would go out and get game and gatherers who would collect wild plants.
That only really changed in the past hundred or so years.
The exception was in Feudal Europe where all game belonged to the landlord. Even there though the gathering and fishing continued.