I have to correct you on this statement. People did not do things because they only thought they would work, they did them because they worked for them over time, i.e. they approached their practical affairs scientifically even before that term was trademarked. For example:

Hasan Ibn al-Haytham (Latinized Alhazen) 10–11th century Islamic scientist. “He was also an early proponent of the concept that a hypothesis must be proved by experiments based on confirmable procedures or mathematical evidence — hence understanding the scientific method five centuries before Renaissance scientists.”

Note the standard of evidence in the quote above. It is not just “doing experiments,” it’s “confirmable procedures or “mathematical evidence.” People always have done experiments. Basic farming requires it, and the rise of civilization evidences the practice. Furthermore, the experiment that you reference didn’t usher in a new way of “doing science,” it ushered in a new way of selling science:

Galileo returned to Florence, where he might have been expected to continue his scientific research. But for about two decades after 1611, pure science ceased to be his main concern. Instead, he became obsessed with converting public opinion to the Copernican system. He was an early instance of that very modern type, the cultural politician. All of Europe, starting with the Church, had to buy into Copernicus. This crusade would never have ended in the offices of the Inquisition had Galileo possessed a modicum of discretion, not to mention charity. But he was not a tactful person; he loved to score off people and make them look ridiculous. And he would make no allowance for human nature, which does not easily shuck off an old cosmology to embrace a new one which seems to contradict both sense and tradition. (https://www.catholiceducation.org/en/controversy/common-misconceptions/the-galileo-affair.html)