The real scientific method is the inductive method invented by Socrates and elaborated by Aristotle, Bacon, and Whewell. It is different from the hypothetico-deductive method invented by JS Mill in the 19th century which is passed off as the method of modern science.
Consider Francis Bacon. He called immature concepts “notions”. Induction starts with notions from common experience and iteratively improves them using sense experience until the form or essence is identified. This form is the cause in the full sense of the word; the form is what something truly is — and so should be defined as such. Thus the induction is true by definition. Sound circular or trivial? It’s not because getting the concepts right is what inductive science is all about.
William Whewell described two complementary processes, the explication of conceptions and the colligation of facts: To explicate a conception is to clarify it by identifying what it contains, by unfolding it, for example by surveying and examining examples. The end result is a careful definition of the conception. Colligation is the complementary process of binding facts together by means of a precise conception. The result is an induction, which is the narrowing of a generalization until it is exact and universal.
Yes, induction leads to hypotheses and testing but this is for the purpose of finding the consilience of inductions, the confirmation of inductions in different and multiple ways. The key step takes place before hypotheses and testing: the discovery of a conception of the facts that binds them together.
This understanding of induction was lost in late antiquity until Francis Bacon restored it and laid a foundation for science that lasted two centuries. Then in the 19th century Richard Whately and JS Mill replaced it with a different method, one that came to be called the hypothetico-deductive method, which depends on uniformity and naturalism, and is conceptually confused and logically deficient.
John P. McCaskey and others have explained the history of Socratic induction in science. As examples he gives cholera, electrical resistance, and tides (see here).