Science is the application and result of the scientific method. Without the scientific method, there is no science.
You can observe all day long, study all you want, and conduct as many experiments as you like, and use whatever system you want, but if the scientific method is not applied, then it's not science. It's psuedoscience.
I would like to agree with this. However, I think it is worth pointing out that there technically is no singular scientific method.
Yes, the core of science is done by creating models which give us hypotheses and we develop experiments in an attempt to falsify these hypotheses. However, not all of science is this straightforward.
Some of science is done by researching new data without a hypothesis at all. Some of science is done by analyzing the experimental and research data that has been gathered in order to form conclusions that do not quite reach the level of a model. It is also worth noting that some scientists are focused almost entirely on theoretical disciplines and conduct no experiments themselves, sometimes with doubts about whether their models are testable at all, such as in the case of String Theory.
I propose that science can be better thought of as composed of four primary philosophical elements; empirical investigation, methodological naturalism, epistemic humility, and critical rationalism. It is from the combination of these four philosophies that we can ascertain the common, simplified notion of a "scientific method" but the actual philosophy of science is more complex than that.
Of course, in practice, there is a distinction between "science" in the sense of the philosophy of science and "science" in the sense of the academic sciences. The latter is where doctorates, peer-review, scholarly journals, university funding, and so on are involved.
Anyone who practices the former (philosophy of science) without being a part of the latter is called an amateur scientist, which some might argue is not a scientist at all. (ETA: Although people in this category are also sometimes called skeptics, critical thinkers, and freethinkers, too, and they tend to congregate in skeptic movements.)
Many people in the latter category (academic scientists) are not well-read on the philosophy of science or do not consistently adhere to it outside of the confines of their job, despite using developments in philosophy of science like Popper's principle of falsification in a narrow, formalized way in their career. This is why we have figures like Michio Kaku who is quite capable in his own field but often peddles pseudoscience regarding fields outside of his own expertise. This is mostly a good thing; it means that individual scientists are free to have a diverse range of beliefs and worldviews while still being able to contribute to the growing body of human knowledge. The downside is that lay folk can make arguments such as, "this neuroscientist believes in an afterlife, so that means that an afterlife is compatible with science," which is completely and fundamentally wrong.
Ideally, academic scientists would have a firm grasp on the philosophy of science and how it relates to their field. Universities do generally touch on the subject in doctorate programs, but I think many scientists end up forgetting much of what they learned, do not know how to cohere their intellectual knowledge with practice, or simply manage to get through doctorate programs without ever fully learning these fundamental concepts to begin with due to the subject not being fully taught or not being a major part of their grade. And, honestly, why would it need to be? The doctorate shows that they are capable of holding a career conducting research in their field, and that's enough for the practice of science.
This is a long way of saying that I think it's worth remembering that science is a lot more messy and nuanced than the concept of a unified "scientific method" tends to imply. We can keep talking about a scientific method, of course, but I think we need to keep in mind that it is an oversimplification that comes with baggage and qualification.