Goats are small enough that three people could easily milk it with
domesticating it: One to hold the front, one to hold the back and one to
milk it. This would require no tech of any kind, not even that sharp stick.
One reasonably strong (and hungry) person could probably milk it without aid
from anyone else.

On the other hand doing so with a full grown cow would require a lot more
than three people.

I think it's reasonable to believe that humans where consuming goat milk
prior to domestication but that cows milk wasn't regularly consumed until
after domestication.

-Tad