How did the first humans to grow food figure out the concept of farming?

The Babylonians credited Ninkasi, the goddess of beer. Barley was the first cultivated crop. Hoist a stein to her for starting us on the road to civilization.

Humans have probably always understood the concept, but it was grain that caused the big advances in farming, because grain can be stored for a long time without spoiling and also bartered for other products.

Animal farming is probably even older, imagine a hunter killing a sow with piglets, it would make sense to keep the piglets alive until they became big enough to eat, and the next step would be to breed them.