What almost certainly happened was that bronze was stumbled upon by accident and then refined by trial and error because someone saw it's possibilities.
So the question is when does personal experience become experimentation?
Very infrequently, especially outside the realm of infants and young children.
The main difficulty in this debate is the melding of the terms 'science', 'scientific method' and 'experiment', with people behaving as if they are all fairly synonymous. They aren't. It is possible, for example, to have a science which is incapable of conducting formal experiments. Astronomy is as good an example as any: it is impossible to 'trial and error' astronomical observations, instead you have to rely on searching for and spotting the phenomenon that provides evidence that your hypothesis is not incorrect.
In fact, 'trial and error' in the usual sense is not generally used in scientific study, except in limited situations or at the very beginning of examining a given problem. It also features more heavily in the
applied sciences, for example searching for a new antibiotic, where a variety of chemicals might be trialled-and-errored in the search for one with the required properties.
To relate this to cycle helmet design and testing: You wouldn't, for ethical reasons if nothing else, try to find a useful head-in-bicycle-crash-protection-measure by dropping real people on the crown of their skulls whist wearing a variety of headgear from a given height. That might 'prove' that a watermelon helmet has less impact absorption than a Styrofoam one (or not, as the case may be), but it wouldn't tell you very much about all the disparate variables that might be in operation during a genuine bicycling crash with attendant head-impact-on-tarmac.