Oh dear, another sad attempt to try and conjure a 23 centuries old piece of rhetoric into physical reality.

Let us agree that science is our best method for establishing reality

So why do you spend so much of your time, constructing apologetic fabrications to try and conjure fantastic magic entities into existence?

Plus, scientists don't "establish" reality, they describe reality, based upon the observational data being surveyed. As I keep telling anyone who will listen, science is DEscriptive, NOT PREscriptive. A distinction which is apparently too hard for some supernaturalists to understand, having spent their entire lives wasting their time with PREscriptive mythologies.

A scientific principle isn't a "decree" handed down from on high, it's an exposition of what the data is telling us. I know that supernaturalists, with their background of treating apologetic fabrications as fact, and mythological assertions as true just because their choice of mythology presents those assertions, have a hard time with this elementary concept, but science isn't in the business of "decrees", it's in the business of asking "what does the data tell us?" Which, wait for it, is why scientific theories change the moment the data tells scientists that this is needed. See, for example, the transition from Newton to Einstein, a transition about which I've written much in the past.

Let us agree that if there was an uncaused first cause

That's almost as big an "if" as "if there was a magic man". Not least because everyone here knows that this is where this is leading. The agenda is nakedly transparent.

Plus, I've already pointed out that quantum mechanics has pretty much tossed classical causality into the bin, unless of course, you can tell us what "causes" a particular atom among billions in a lump of radioactive material to decay at any given time. If you can't, then you're in a spot of bother trying to use classical causality to try and conjure your imaginary magic man into existence, when said classical causality has been stomped upon Godzilla style by quantum mechanics. Not least because, wait for it, classical causality is deterministic, and indeterminism rules on a grand scale in the quantum world. Worse still, there exist systems that, even though they're macroscopic, and therefore tend to the classical limit, exhibit extreme sensitivity to initial conditions, rendering attempts at prediction of future behaviour of those systems null and void. If a system takes two divergent trajectories, from initial conditions that differ by an amount too small for you to detect or measure, then even some supposedly classical systems have to be treated as indeterminate over the long term. Which again buggers your apologetics on a grand scale.

Oh, and there's the little matter that the "uncaused first cause" assertion violates the initial premise of the entire argument. Said premise being that all entities are the product of a causal agent of some form, without exception, only lo and behold, for the exception violating this premise to be presented as a purported "conclusion" arising therefrom. As a corollary, this piece of apologetics isn't an "argument", it's an exercise in paradox.

it would have existed before the universe

And here again, we see the typical supernaturalist failure to apply rigour.

First of all, as I've already stated, one needs to exercise rigour with respect to what one means by the phrase "before the universe" in this context, which requires that there existed a metrical frame and an arrow of time prior to the instantiation of the current observable universe. Which means that any attempt to bring in Augustinian assertions about a magic man being "outside time" start to look ridiculous. That's before we factor in what I've said earlier about entities and interactions prior to the Big Bang being an active research project, with no one participating therein thinking that a magic man is needed.

Therefore, how do you atheists know

Actually, even any of us who happened to be tenured cosmological physicists, would tell you, yet again, that we don't actually know, and that the requisite matters are, yet again, active research topics. Once again, this isn't the province of "atheism", it's the province of cosmological physics, and I suggest you find some cosmological physicists to educate you on this matter.

that sciences such as logic

Logic isn't a "science", it's an abstract formal system, and properly the remit of pure mathematics. Do learn the elementary concepts applicable here.

Plus, in the case of an abstract formal system, its rules would apply to the abstract entities within its own abstract space, regardless of what was going on in any concrete realm. Again, what part of this elementary concept do you not understand? Just as, for example, 2+2=4 in the real number field regardless of whether or not a physical universe exists. It's a consequence of the axioms of the system.

entropy

Entropy isn't a "science", it's a physical quantity. It even has SI units associated with it - joules per kilogram per Kelvin.

Oh, and Ludwig Boltzmann might want a word with you, with respect to the matter of what entities, and what states thereof, would be applicable in the requisite scenario, which is one of the reasons why, once again, the presence of entropy in a pre-Big-Bang scenario is an active research topic. How many times do I have to stamp the words "active research topic" on your fucking forehead, before you get the fucking message?

and thermodynamics apply beyond the universe?

All together, boys and girls, once again ...

THIS IS AN ACTIVE RESEARCH TOPIC!

And once again, boys and girls ...

THIS IS THE PROVINCE OF COSMOLOGICAL PHYSICS, NOT FUCKING "ATHEISM"!

Going to learn the requisite elementary concepts here, are you?

@Cali! I love it. Whenever you get so fucking tired of saying the same thing over and over and over and resort pejoratives, it always brings a smile to my face.. It's like eating sausages and vanilla ice cream for breakfast.

***Viewer Discretion Advised***

@Reed Re: OP - "I just need to understand something using logic"

Somehow I get the feeling you would not know what logic was even if it fucked you in the ass with an eight inch porcupine dildo.... *being tapped on shoulder by Cog*... *leaning back and listening as Cog whispers in ear*... *turning to look at Cog incredulously*... Really???.... *Cog silently nods head*... Well, okay. If you say so... *returning to post*... Hmmm... It seems my remark could potentially be considered as "too graphic" for some viewers. Oh, well. Whatever... *shrugging shoulders*... Fine. I'll just put "Viewer Discretion Advised" at the top of this post. Anyway, in my defense.....

Re: "Therefore, how do you atheists know that sciences such as logic, entropy and thermodynamics apply beyond the universe?"

...I think that statement right there pretty much helps demonstrate the justification for my remark. I rest my case.