When I follow discussions between atheists and enlightened catholics, I notice that they often talk past each other, due to entirely different ideas about what is meant by 'God'. After I found God for myself (not a religious one, but an Aristotelian one), I discovered that there are at least four different aspects of the God concept, which involve quite different assumptions. (This is not exhaustive in any way, of course.)
These are the Four Gods:
1. The God of a religious, institutional narrative. This is a (often personalized) entity with distinct properties and duties that are documented in canonical teachings. Typically, this entity holds strong opinions about the morality of individuals, metes out rewards and punishments, and his prescriptions tend to be aligned with certain political and societal goals.
2. The God of the spiritual experience. This god is the principle of a universe that is intentional, is conscious, and usually partial towards the individual, but reveals itself independently of allegiance to any religious institution. You will often find that this principle is benevolent and loving, and its interests are well-aligned with your values (see Deepak Chopra), but that is not necessarily the case (Philipp K. Dick's god of 'Valis' comes to mind).
3. The principle of transcendental meaning: God is the question that the universe answers. In the weakest sense, this god is the reason why there is something rather than nothing (an ontological duty that hardly conflicts with any expected future results of scientific inquiry). However, it implies a telos, i.e. the universe inherits a purpose. I think this is the god of Thomas of Aquinas, as apparent in his Fourth and Fifth Proofs for the existence of God.
4. The Prime Mover: rather than assuming that physics is entirely self-contained or that the universe is essentially static (and only appears to be moving due to the way we observe it), there must be something that moves things along. This first mover (primum movens) is arguably the god of Aristotle.
When atheists attack theism, they usually focus on the gods of religious narratives. These gods often do fascinating, highly surprising things, such as manifesting as talking shrubbery, killing first-born sons, sending bears to kill uppity children, impregnating virgins, prescribing colonial wars or resistance against imperial forces, and dictating religious scriptures to enlightened prophets.
Believing in such a god requires a belief attractor, i.e. there is an intrinsic part of the religious practice or belief that makes it subjectively or objectively very expensive to let go of it (such as threat of eternal damnation, social ostracism, etc.).
When the duties and preferences of such a God collide with scientific theories (such as the creation of species), modes of political administration, default societal norms (sexuality etc.) conflicts ensue. Large religious institutions have a process in place that subtly updates the interpretation of religious doctrine to reduce such conflicts. In the absence of stringent institutional enforcement, individual believers perform these repairs by themselves, too, often even bridging across competing religious institutions. However, all large institutionalized religions also have spiritualist and intellectualist schools, where the former focus on the practice of direct, individual spiritual experience, and the latter may turn God largely into an epiphenomenon or even completely non-ontological. Especially non-ontological theism is oblivious to the arguments of unsophisticated atheists.
The spiritual experience is part of the human condition, and it is tempting to interpret it as indication of a transcendental consciousness, rather than an artifact of our cognition. The spiritual god resonates with deep needs of many people, and its experience may be evoked in psychedelic and meditative experience. Opposition to the spiritual god is usually motivated by an absence of personal spiritual experience, by a strong dislike of Deepak Chopra, or on epistemological grounds (experience certainly says something about our mind, but not necessarily about the nature of the universe).
The god of meaning may not offer salvation, moral direction, or practical insight, but marks the last line of defense between a ruthlessly honest inquirer into the nature of things and nihilism. The god of meaning has no knowable features. However, it is not generally accepted that even such a god can be inferred (as Thomas of Aquinas famously did). I agree with him that it is possible to build a logic in which each statement is defined as the answer to a question. In such a system, anything in existence allows the inference of something that invokes it, and eventually leads to the inference of a question outside of the system, which we may call 'God'. However, in our common ways of defining logical frameworks, this is equivalent to hiding God in an axiom that we have deliberately put into the system. Since we are free to pick our axioms, we are stuck with God OR NOT God, which does not allow to infer God, but only God OR NOT God. Thus, our universe does not contain necessary Gods, only possible Gods. Aquinas' God is a necessary one, and hence he does not exist ab initio in an axiomatic framework.
Our cognitive processes are producing answers for complex control problems of our organism. We may possibly understand our consciousness as such an answering mechanism: as the many-layered, continuous attempt to discover the nature of our existence. In this sense, consciousness might be analogous to a logic that sees every sentence as an answer to a question, and God may be referenced as the natural cause and purpose of our existence, i.e. a reference to a transcendent process that manifests as an intuitive necessity, a sense of meaning pointing beyond our universe. This does not constitute God as an ontological phenomenon, but as a cognitive one. If we deny God's existence as a source of transcendent meaning, we turn (like me) into ontological nihilists, but we do not need to turn into cognitive nihilists. The absence of meaning in my universe is not reflected in an absence of preferences and values. (Preferences are cognitive mechanisms that let me choose actions based on expected pleasure and displeasure; values are cognitive mechanisms that allow me to choose unpleasant outcomes.)
I find that in contrast to the god of meaning, the unmoved god of movement may be an ontological necessity. The universe manifests itself as a set of discernible differences at our systemic boundary, which is to say, a vector of bits that our mind interprets as its current state. This current state contains the past as memories, and the future as possibilities, and possibly even ourselves as the structure of an interpretational system, and yet it does not suffice to account for any conscious experience. Consciousness is intrinsically a process, spanning more than one state. To notice that we are conscious, we must be able to access patterns of information that we may interpret as past world states, along with other patterns that we may interpret as different past world states, and in comparing them to experience that a progression of states takes place. A progression of states requires a principle that allows for transition from one state to the next. This is reflected in our definitions of computation, which are based on states that are ordered by a transition function.
In other words, the universe does not manifest itself as a giant pattern of bits, but as a succession of patterns, which means that something must progress from one pattern to the next. Some function, outside of the context of the state of the universe, must push the tensor network we tentatively call reality from one moment to the next.
The computations of the universe can in principle not be self-contained. If the universe contains mechanisms that allow it to compute, then something must act as its computational substrate that moves the computations of the universe along. There is of course nothing we can say about this computational substrate, except that it realizes a transition function capable of moving the universe from one state to the next. This outermost mechanism does not exist in space or time; rather, its state successions give rise to space and time, and all objects that appear to populate our animated universe. Compare to Aristotle:
It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor is there any change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most self sufficient of lives… From [the fulfilment of the whole heaven] derive the being and life which other things, some more or less articulately but other feebly, enjoy.
— Aristotle, On the Heavens, I.9, 279 a17–30
Without this Prime Mover, nothing in the universe could progress, computation would be impossible, we would not have minds, and hence could not have a conscious experience of a dynamic or even static universe. It may be tempting to conflate Aristotle's god: the Turing machine that runs the universe, with Aquinas' god: transcendental meaning and purpose, or even with a spiritualized god. But such an attempt seems to be epistemologically dishonest to me.