Im gonna quote Oxford University and Nobel prize winner, and mathematical physicist Roger Penrose:
“Try to imagine phase space… of the entire universe. Each point in this phase space represents a different possible way that the universe might have started off. We are to picture the Creator, armed with a ‘pin’ — which is to be placed at some point in phase space… Each different positioning of the pin provides a different universe. Now the accuracy that is needed for the Creator’s aim depends on the entropy of the universe that is thereby created. It would be relatively ‘easy’ to produce a high entropy universe, since then there would be a large volume of the phase space available for the pin to hit. But in order to start off the universe in a state of low entropy — so that there will indeed be a second law of thermodynamics — the Creator must aim for a much tinier volume of the phase space. How tiny would this region be, in order that a universe closely resembling the one in which we actually live would be the result?”
“His calculations lead him to the remarkable conclusion that the ‘Creator’s aim’ must have been accurate to 1 part in 10 to the power of 10 to the power or 123, that is 1 followed by 10 to the 123rd power zeros.”
As Penrose puts it, that is a “number which it would be impossible to write out in the usual decimal way, because even if you were able to put a zero on every particle in the universe, there would not even be enough particles to do the job.”
And the only alternative to the universe arising from chance is for it to have arisen deliberately. Deliberate action requires a conscious creator aka God.
Hello, nice question!
There are a few ways to try to offer other perspectives to compare with the one being attributed to Penrose.
Unless you have a degree in the hard sciences (some few of us do, (myself I'll admit) but most would not), this writer also might be of interest, along the same question:
A Universe with too much matter-and-energy for its expansion rate will recollapse in short order; a Universe with too little will expand into oblivion before it's possible to even form atoms. Yet not only has our Universe neither recollapsed nor failed to yield atoms, but even today, some 13.8 billion years after the Big Bang, those two sides of the equation appear to be perfectly in balance.
If we extrapolate this back to a very early time — say, one nanosecond after the hot Big Bang — we find that not only do these two sides have to balance, but they have to balance to an extraordinary precision. The Universe's initial expansion rate and the sum total of all the different forms of matter and energy in the Universe not only need to balance, but they need to balance to more than 20 significant digits. It's like guessing the same 1-to-1,000,000 number as me three times in a row, and then predicting the outcome of 16 consecutive coin-flips immediately afterwards."
The Universe Really Is Fine-Tuned, And Our Existence Is The Proof (forbes.com)
So, there is one figure:
probability < 1 in 10^20 (note even 10^-20 is still an astoundingly small order of magnitude)
For another number (link below), we can consider a reason to expect a lower boundary:
probability > ~ 1 in 10^500
(an award winning science writer, at what is probably the top site for physics developments reporting long with sites like Phys.org) --
Complications in Physics Lend Support to Multiverse Hypothesis | Quanta Magazine
In this article you'd see why 10^-500 is a reasonable number to consider also as a boundary number, but
more importantly why we
cannot conclude anything one way or the other about the reality that our particular (local!) Universe is definitely
"fine tuned" (*) and
"unnatural" (*).
(* --
quoting physicists)
In short, no one can prove or disprove God's existing through physics.
If someone could, God would be surprisingly allowing a loophole in the conditions He has set for us to face in our mortal lives: That we must chose whether to trust Him or not -- aka
"faith" -- which is to believe
before proof.
I cannot achieve a condition of faith that I have a car, since I can simply observe the fact, without any choice to believe.
If proof was available before belief, then that would preclude the chance to have
faith, it would obviate faith.