Galileo was the first. All the others you mention followed him, except Kepler, his contemporary, who developed empirical laws based on observed data. He never conducted any significant experiments. His primary achievement was his empirically derived laws for planetary motion.

Scientific method as a philosophical procedure can be traced back to Roger Bacon in the 13th century, who had access to the writings of antiquity provided by the Arabs. But it was Galileo who rolled balls down inclined planes and timed pendulums with his pulse. And after him, modern science exploded across Europe. But I think the true origin of science came much earlier, from the Ionian philosophers.

Prior to them, the world was the anthropocentric creation and playground of man and the gods. It was all spirit and thought, dreams and essence. The Greeks invented our modern concept of "nature", they posited a reality independent of the mind, the senses, and divinity; it operated on its own laws and they were understandable through observation and reason. Even the gods were bound by these laws. No one else anywhere had ever made that leap, even civilizations like the Chinese who had superior technology, and even the Greeks abandoned it after the success of Platonism.

Other civilizations had great accomplishments, but their technologies were developed through purely empirical methods and trial and error. The pre-Socratics were the first to realize that there were rules amd we could learn them. That was the breakthrough. Even so, it took two thousand years before that idea was translated into a set of systematic procedures.

As for theology and metallurgy, it's not clear what they have to do with it.