This is an excellent question! I have pondered this a lot myself and hope you can take some benefit from my approach on having answered this for myself, depending on the degree of how well I manage to bring my point across. I wish for this to become a discussion.
I have to say beforehand, that I am neither a christian, nor do I belong to any other religion. Science has always been the most important resource for me, because I dont't think there is anything not possibly being answered by science.
This Sean Carroll's notion about the impossibility of "god" and a life after death is sadly unscientific. Because the main principle of proof for a hypothesis is the falsification of the opposing null hypothesis. (I get why he is sure about this being correct, but this is based on a problem, which I will address very soon.)
The existence of a superior deity and also the possibility of life after death cannot be ruled out completely, because therefore it would have to be proven in a way that somebody would die and then come back and report, that there is absolutely no existence after death. This is impossible, so the null hypothesis cannot be proven ergo the hypothesis of a life after death cannot be falsified. When it comes to god, this would be way more complicated and this brings me to the point of why this astrophysicist might think he has falsified the hypothesis, so the nullhypothesis -the nonexistence of god- is proven.
I believe this and the general pull of most educated people towards atheism lies in a wrong idea about the whole concept of god. The monotheistic religions have implanted an idea of some sort of anthropomorphized god but by doing so have violated this commandment, that "you should not have an image of god" or whatever it is called. On the one hand this might have had the meaning of forbidding tin gods or idols, but in my concept, this is also because "god" could not be imagined in it's entirety, therefore any sort of trying to imagine it would lead to an incomplete picture and therefore a wrong notion of it. It even goes further: What do the religions tell us about the qualities of "god"? (damn I hate this word simply for the wrong associations attached to it, that's why I put it in "" always")
It is said, that "god" is omnipresent, omniscient and all-loving.
Is there anything we know or believe to know from our science, that is omnipresent? Yes there is: The nothingness! If you look at the nothingness substantially, it has no end of expansion. Even billion times wider than the known universe, there is nothing, even before the big bang has occured, there has had to be nothing, every molecule consist of 99.999% nothingness and the atoms and subatomic particles also consist of 99.99% nothingness, maybe even the quarks (we'll probably find out somewhere along the line). So all of the known physical universe is simply a little bit of oscillating energy encompassed by nothingness, which is omnipresent. Even if something was 100% dense in whatever small place in the spacetime, the nothingness would still be like the canvas that this material object is placed upon like the paint of a drawing.
That brings me to the second quality, the omniscience.This gets a little tricky because if you think about something knowing something, you would have to attribute human conciousness to it. In this thought-experiment try not to do so... If all of our perceived existence is encompassed by this mysterious nothingness, that would mean everything that happens, has ever happened and will ever happen, is a part of this infinite "object". Now one could say "But I have also a lot going on in my body on the cellular level and so on and I don't know all of what is going on there". That is only because our concious mind is just a part of our being as a human. We are not just what is happening in our mind but every physiological process belongs to us as well.
(Damn this point is a little hard to bring across....)
So even though we are not conciously aware of every process that is going on, there are parts within us that are noticing them. Maybe not even on the level of the afferent nervous cells but e.g. when an ion dissolves in water, even though it might not have the capabilities to process this mentally or reflect upon it, it is very well aware of the process taking place. And so is everything in the universe on every level of microscopic and macroscopic aware of what is going on. And since the nothingness is both infinitely big and infinitely small at once, every process within existence is somehow noticed by this instance, since it is all happening on this canvas.
The idea, that this canvas has to be thinking and reflecting about how the paints on it merge into other colours is unneccessary for it to be said, that there is a materialistic notion about this process taking place, ergo knowing.
I hope you could derive what I was trying to say here, it was really difficult to bring across because there are quite a few counterargument that could be brought up which I tried to adress already with it...
The next described quality of "god" is the concept of all-lovingness and should actually be a lot easier.
What is love in it's essence? It is not just an emotion, ergo neurotransmitter release within the brain that leaves one with a nice buzzing in our perception. This is just the effect of love taking place. Generally speaking, Love itself is a connection. This connection leads to some sort of reaction usually, within humans at its peak in procreating. Love is one person being pulled towards another. On a microscopic level, negatively charged ions are also pulled towards positively charged ions and within a discharge of energy there happens a reaction in which a bond is formed. The correlation I try to bring up is quite obvious here, right? On a macroscopic level we could talk about gravity, which by the way is not at all understood yet, still no scientist would ever negate its existence. So just because two objects have a mass, they are pulled towards another and this is actually an unlimited force. I mean, the gravity that you emit is still pulling on any object a couple million lightyears away. Not as strong and there are counterforces which stop you from being pulled towards the next blackhole but still, gravity is a force that is detectable through the entire universe. If we go back to the idea of the nothingness now, it is obvious that because it is an all-encompassing object, everything within the universe is connected through this substance. And every object is 100% encompassed by it and cannot be detached from it. Doesn't that fit my abstract definition of love quite perfectly, because there is also a constant reaction going on within even the most inanimate objects and the space that they are encompassed by on the macroscopic and even lowest subatomic levels. We don't have an explanation to why electrons are moving yet, maybe it is the nothingness that is being responsible for a little spark of every matter to be propelled into oscillating.
The last point is probably a little vague, but I guess you get an idea of how you can very easily use science to form a cosmology that doesn't contradict the notion of a superiour all-encompassing "entity". I could go on and on about this, there is actually no end to how I could apply this sort of cosmology, which I like to call "neopantheism" on everything that exists. I hope you will respond to my post in some way and we can discuss this further.
I call this believe, which actually to some degree most people that call themselves atheists (yet admit that they believe there is something bigger, just not a whitebearded guy in the clouds) also share, neopantheism, because it tries to explain the existence through the known nature being "god" and this known nature has expanded a lot through science.
A short notion on this issue of life after death: I had an NDE once and it actually was exactly how it is displayed and described everywhere. But this doesn't mean that I believe in life after death. I think it is both possible, that there is an end to our existence completely, when we die or that it goes on in whichever way. But I think humans should not and cannot know 100% for sure, because it would take away meaning from life. If you knew you would life forever, this day here and now wouldn't matter as much as without the certainty of existing further on but the possibility of dying in an accident tomorrow and it all being over forever. Ergo - seize the day! :-)
Thankyou for writing an extensive post with great clarity on a difficult topic. I truly appreciate the time and and effort it has taken you to do this.
I will be pondering these points for a while. Already read the post 3 times. I will see where this takes me.