Existential writers such as Søren Kierkegaard claimed that proof of God cannot be the outcome of a logical argument, such that God’s existence can never be a public or objective truth. Belief in God, consequently, must always be a private matter, entirely subjective and a function of the individual accepting such truths for themselves as a matter of faith. Hence attempting to prove the existence of a God via such means as the Argument from Design would not fly in Mr. Kierkegaard’s neighborhood.
However, the way I see it is that the way most people accept the existence of a God is along the lines of believing something far less profound, e.g., believing that the earth is round. One accepts this to be a true fact about the world since it fits in with what you have been told about the world, from the time you heard it first mentioned, from what you heard at school or from what you have read about it. As such, accepting the truth of such a belief and most other beliefs one holds as true is a function of coherence with other beliefs that seem to support it, giving you no reason to examine it critically or ever doubt it for that matter.
I’m willing to concede however that – when people say they believe in God – they might be expressing more than just something that they have always accepted as true, such as the belief that the earth is round. What may be referred to as “spiritual beliefs” are the results of having a sense or an awareness that one is part of something larger and more profound than oneself while being unable to cite the specific reason for believing this to be a true belief about themselves and the world. An example of that might be what Einstein wrote about in a November 9, 1930 New York Times Magazine article titled Religion and Science in the context of what he referred to as “a third stage of religious experience”:
I shall call it cosmic religious feeling. It is very difficult to elucidate this feeling to anyone who is entirely without it, especially as there is no anthropomorphic conception of God corresponding to it.
Beliefs based on such feelings may have some intrinsic credibility based on the phenomenological nature of our everyday experiences, when one is led to expect a greater context for them beyond the immediacy of the present moment and whatever else one might bring to bear on them. It is within this expectation or awareness that one might ascribe to the possibility of a deity existing, especially when one is told from day one that there is such a thing as an all-powerful being named God, and being at the receiving end of a process I call “religious brainwashing” at the hands of some authoritarian religious institution that does not allow its core dogmas to be challenged.
Given this line of reasoning, you could say that the belief in God merely fills the void in one’s belief system that resulted from sensing the larger whole of one’s existence without being able to articulate exactly what that is.