When man discovered how a cow gives milk, what was it looking for?

Answer

The first people to keep livestock probably watched small baby animals drink milk from their mothers after they were born. Probably one of the first people wanted to taste this milk and found it very tasty, after which this custom became more and more common.

So the first people probably copied how this worked from small animals that drank from their mothers. After all, people also feed their babies with milk, so they must have found this quite normal.