When you say you "believe strongly" in the scientific method, are you acknowledging a certain kind of faith? A faith that only things which can be proven by the human senses matter? That the collective sense-knowledge of humanity serves as the final authority on what does and does not meaningfully exist, what is and is not significant?
Given all that I know of human beings - by my own observation and study, in addition to the findings of psychologists, anthropologists, historians, biologists, etc. - I would not trust that a race of beings who are so finite, limited and error-prone could hold the keys to everything. In order to do this, I would have to presuppose that the race (or at least its educated leadership) is correctly interpreting the cosmos, concerning both the things seen and the things unseen. Since the universe is so vast, and our window on it is so tiny, how can we place so much trust in our own perceptions?
The strength of this position is that things known are known with absolute certainty (e.g., that rock is a rock, made up of these elements, having these properties, and it always behaves in these ways, no matter what). The weakness is, larger questions are left unanswered - there are so very few things that can actually be known with "scientific" certainty. A true agnostic has to disbelieve so many things which would seem to be self-evident, simply because they are not scientifically warranted.
However, I do not believe anyone really lives by these principles. There is a presupposition that God either does not exist or has no interaction with the world. Hence, divine creation is not even entertained as a possibility, and evolution is assumed because it is the only possible way life could have arisen without divine action. And when the obvious question is asked, "Where did the original particles come from?" the answer is: "We don't address that question, it can't be known with any scientific certainty." And yet there is a certainty about the idea that there is (essentially) no God (at least no meaningful God), and He couldn't possibly have intervened in the universe in the distant past (let alone have created it). But I say, "What if there is such a Being, and He really did those things, and He is simply beyond the reach of human perception?" Although this cannot be known with scientific certainty, it is equally true that His non-existence and non-interaction cannot be known with scientific certainty. So, when it comes to the big questions (the ones not discernible by science), all of us are left to faith and presupposition.
Imagine, for a moment, that mankind had no sense of taste, touch, sight, smell, or hearing. Would everything that is now scientifically verifiable cease to exist or have meaning? Would everything be meaningless until observed? Even if we had no means of observing it? That would be absurd, like the old question about a tree falling in the woods! Yet this very assumption is made, that there is no meaningful God because we cannot observe Him scientifically.
I love science and agree with its observations as far as they go. But is it wise to conclude that there are no meaningful realities beyond the scientific facts? Are there scientifically valid reasons to assert this? I believe there are scientifically valid reasons not to assert it, and even to vehemently deny it. One observable, repeatable, and established fact proven by science is that there is much more in an unsearchable universe than science has ever discovered or ever can discover. As an epistemic source, I judge it to be highly reliable but far too limited. Like a very solid and well-built bridge that only goes a few inches across the chasm.