"So we should assume that at no point did it become necessary for humans to research and hypothesize regarding ways to breed animals for a living or make use of metals; that these practices do not involve, and never have involved, science."
Of course not. Humans have always observed the world around them and acted accordingly. They saw that this one ewe produced larger lambs, so they bred more lambs from her offspring. They learned that by observations. Same with metals. The bronze from one mine was stronger than the bronze from another mine, but the other mine's bronze was a more golden color. Observation.
Thing is that science is more than just observation. It is a precise system for forming hypotheses based on information, then testing those hypotheses.
Science grew naturally out of the experiences of mankind. Sometimes, though, religion got in the way of that growth, making it take a bit longer for real science to appear.
But, what the bronze age folks were doing was not science. It was observation and trial and error. It worked OK, but wasn't science.
I give you alchemy as an example. It didn't work. The techniques of alchemy, however, became useful once the idea of testable hypotheses came into play.
Science is a system. Without the system, science does not exist.
Science is "the observation, identification, description, experimental investigation, and theoretical explanation of phenomena." It began with the first humans. It is not as if a certain amount of precision is needed and then *VOILA* it's real science.