There is no such thing as the "scientific method." Scientists use many different methods, engage in many different kinds of activities, and ask many different kinds of questions. What defines science might best be characterized as an attitude -- an attitude that is more about what it forbids than what it enables. The scientific attitude is that the only legitimate way to answer any scientific question is to observe reality -- the truth is out there. The ultimate test is that if more and more people follow the same observational procedures, what they see will be the same.
That may strike you as banal, but it was a most uncommon attitude, in fact largely non-existent, for the first 300,000 years or so of the existence of Homo sapiens, and it is still actually fairly uncommon today. A few of the ancient Greeks engaged in what we now call science, but for the most part the Greek philosophers engaged in very different activities. They essentially invented ideas by introspection and imagination, and argued for them on largely esthetic grounds. Thus the universe was made of earth, air, fire and water; or may just air, or just water. Aristotle was fond of what we call teleological explanations -- things are made in a way that serves a purpose. It is the nature of things to want to be in the center of the universe, which also happened to be the center of the earth, which accounts for the downward pressure we call gravity. But it is not the in nature of the celestial spheres to want to be there. Living things are animated by a force that seeks their ends, whatever those may be.
In Europe a few hundred years later, everybody knew that God made the world, and that the purpose of humans was to worship God, obey his laws, enrich his priests, and serve and obey the nobles who ruled by his divine will. What was known specifically about practical matters was to be found in authoritative ancient texts, including Aristotle and the Roman era Greek physician Galen. As feudalism gave way to nationalism, the imagined community of the nation state gave a new kind of meaning to existence, even as people gained more choice of religions, although not having one at all was not considered a legitimate choice.
A few thinkers who were ahead of their time -- Francis Bacon -- began to express something like the scientific attitude as early as the 17th Century, but it didn't really start to catch on until what we call the Enlightenment of the 18th and 19th Centuries. The word "scientist" was coined by the Cambridge academic William Whewell in the 19th Century. Galileo really did practice science, in the late 16th and early 17th Century, but Isaac Newton, whose lifespan was approximately 80 years later, is credited with being the key figure in the so-called scientific revolution.
Newton was actually devoutly religious, and after hours he practiced rather mysterious inquiries in alchemy. But he is important because he compartmentalized. When he did science, that's all he did, and what that means is that he did not even try to develop any explanation beyond what he observed. Gravity is an attractive force between two masses which is proportional to their total mass, and inversely proportional to the square of the distance between them. That's it. With that equation he could predict the motions of the heavily bodies (elucidated more precisely by Kepler), and the motion of projectiles. He had no idea why this was true, and given that he had no evidence that could bear on the question, he didn't even ask it.
Einstein later concluded that in fact, massive objects warp space-time, and that this accounts for gravity. However, Einstein did not know, did not speculate, and did not even ask why massive object warp space-time. This is the problem with science -- it does not allow for speculation, for what is called metaphysics, and it doesn't offer any meaning or reasons. To many people, that is not just unsatisfying, it is intolerable. They need meaning, they need reasons, and if they aren't getting it from scientists, they'll get it somewhere else.
This is a grave challenge, because, while science has given us the technology that doubled our lifespans and lessened our toil, that same technology is threatening to do us grave harm or even destroy us, and the only way out is to believe in the science that tells us so, and wield its power to save our sorry asses. This was not a good time to make a demented criminal lunatic president.
