I'd like to start this post with an analogy; say you are speaking to a friend who cannot comprehend the idea of a prime number, he is smart in many other aspects, but simply does not get what a prime number is. So you try to explain it to him, you may use examples to prove prime numbers, but he believes them to be non-existent things invented by mathematicians. After a long conversation he asks you to take him to a prime number, to show him one. This is obviously impossible so he concludes that he is right in believing prime numbers don't exist, however we know that prime numbers do exist, this proves only that he has not understood the concept of a prime number.
As you may have guessed, the analogy was of God, I used the analogy here because it shows God as a concept, something to be understood, like the equator, which can be said to both exist and not simultaneously. Many theologians would argue it is impossible to understand God, even through via negativa, as God is so different to everything else in existence, for example our universe is spacial, temporal and variable to change. Whereas God is timeless, spaceless and immutable, (These ideas about God seen in the Christian theology are derived from Plato's “Forms”) It is therefore impossible to describe God within the restrictions of our language as all words meanings change when referring to God.
For example the two statements:
1) Joe is Good
2) God is Good
These two statements completely differ from each other, and not only because of extent, they are good in completely different ways, Joe may be good but his goodness is limited and not pure, whereas God's goodness is not only perfect and everlasting but abstract in a way we cannot possibly understand.
A good way of looking at this is by taking the two statements;
1) A watchmaker is good
2) His watches are good
The watchmaker's watches are good because they are shiny and durable, whereas these traits are not what makes the watchmaker good.
When we accept this point we can then ask to what extent does God ‘exist’, if we take God to be outside time, he doesn’t exist in the real world and can therefore not truly be considered existing. However if we take the traditional Catholic view that God is everlasting, as in living within time but living forever, this brings the question of where time came from, as God is within time and time existed before the universe, so God did not create time, and is therefore subject to it.
"O Sovereign Lord, you have begun to show to your servant your greatness and your strong hand. For what God is there in heaven or on earth who can do the deeds and mighty works you do?”
Deuteronomy 3:24