I'm not dodging your question, just failing to understand it.
Tell you what: can you define for me what you're thinking about when you say "science?" I'll then answer the question.
Otherwise all I have to do is point out that science is a method, so to "prove it exists" all I have to do is point out that said method is possible (it is), and that people utilize said method (they do), and that therefore it exists. As a physics grad student myself, I've done my fair share of the scientific method in labs for various classes, for instance.
Exists within context that is this tangent is that there is physical proof that only points to God as explanation for that evidence. What stands out, often, to me is the 'only' part, for if one says, God is cause / creator of whatever physical process, there are many in room who say that isn't proof of God, for we if we can find another explanation, another way to describe phenomenon in rational way, then it is reasonable to conclude this phenomenon isn't sufficient proof for God.
Okay, so hopefully within this context, that satisfies what exists means.
I would think, though anticipate some debate, that atheism (like theism) wouldn't fit within this version of existence, as both are essentially imagined (beliefs). To whatever degree there is disagreement on this, I'm up for discussing it, especially since it has much to do with this thread.
Science is where I would maintain disagreement, but since it is perceived as method more than 'mere belief' the argument could be a lot more lengthy, while I believe we'd essentially be arguing fundamentals primarily and exhaustively.
To me, science is fundamentally, an intellectual activity consciously designed to enhance human awareness through a systematic process. That is perhaps not dictionary definition even though I'm somewhat borrowing from dictionary. And like all definitions, there is key words that sum up the term in sound bite form. For science, I think that is "intellectual activity." This doesn't distinguish it from other activities that are of the mind, but at a point after definition comes a whole lot of elaboration. IMO, endless elaboration. The very process of science from first time term was coined (in my understanding around 2500 years ago) has constantly been updating "what is science." Yet fundamentally it has not changed from being 'intellectual activity' into something else.
Now, in definition I have above, there is the words "systematic process" and that is where scientific method would fit in. I think many think without method there is no science. I would generally not disagree, though I think that is rigid, or too rigid. A whole lot of things are considered scientific without necessarily having to always apply method. A (recent) example would be:
Your on the internet and chatting which is proof of science
Cause without even seeing response to what I said in reply to this post, I anticipate the response to be along lines of "computer science brought you internet and is proof that science (in general) exists)." Which also coincides with what you said when you said:
people utilize said method (they do)
And this is where I express disagreement based on how I, in this post, referenced "exists." For if you do said method, but I can explain or describe those physical activities in another (rational) way which explains them as not only pertaining to science, then it is reasonable to conclude this phenomenon (physical correlation(s)) isn't sufficient proof for science.
IOW, if one claims to be observing / studying phenomenon in a lab and I describe this as similar to how artists may review and scrutinize and object before depicting it, I will have provided alternate explanation, or depiction, for that activity. Such that it isn't 'only science' that the person is up to. So, then we may say, 'method is a whole process consisting of several steps.' But if at any point of the process I can explain it to be something other than only scientific method, it is plausible whole process is not science, even if practitioner wishes to claim otherwise. They are welcome to that opinion, but it would obviously be bias at work, rather than allowing for data that has clearly shown the phenomenon could be explained / described different (about what observer is plausibly up to).
And another aspect of this is where we allow crafts to be called science. Thus essentially saying nearly all intellectual activity where principles of engineering are anywhere on the radar, gets to be called science or result of scientific method. This is where science gets to argue what it is up to overlaps and perhaps even envelops what art is up to. And to what degree this is accurate is matter of ongoing debate. I think there are several who would say all crafts of any kind do not belong in domain of science. While others say, clearly some do.
And somewhere near the bottom, as was mentioned near the top, we are talking about an intellectual activity which is in the mind. It is imagined, and is not found in the physical world. To the degree it is found, it is only found in human activities. And where the mindful activity becomes practicing of science, it is no different, I would say when mindful activity of say meditation becomes practicing spirituality. Neither is anything more than mental construct of human imagination, but one gets to be connected to 'facts' via bias that is under examined while the other, if ever remotely connected with fact, is scrutinized and deemed only based on feelings and personal experience regardless of the umpteen million people who engage in same activity and find very similar results.
Science as intellectual activity starts in human mind and ends there. Anything perceived as outside of human mind and also deemed scientific is delusion. For the same human mind is capable of presenting alternate explanation(s) of what scientist(s), aka humans, are up to when (allegedly) engaged in methodology. Research and experimentation with physical phenomenon is nothing more than humans interacting with aspects of their environment, while application and production of objects from research and experiments are nothing more than humans crafting physical phenomenon based on human imagination.
