When we look at this question, we have to first be clear on the meaning of word God because this word is used by many cultures in many ways. But basically the underlining idea is God means someone who is almighty and capable of doing everything, God is someone who operates this world, gives rewards to good people and punishes bad people.
The idea of God mentioned above is more like a person doing moral policing than a loving creator of all. So first let's try to come to a understanding which can be more justified towards God rather than making Him a policeman.
If we keep every spiritual thought aside for some time and look at our day to day lives, then some people among us think that because of its complexity, the world is operated by some intelligent person. Some think that there is no need to think like that because this world can be an accident in the immeasurable count of the galaxies and stars. There is no need of inferring any intelligent person behind the operations of this world.
The two thoughts mentioned in above paragraph are opposed to each other and we cannot come to any conclusion by them because both seem right in their own place. So, we should look at our own experience. Now I will try to look at this question from my own experience of world.
Right now while typing on the keyboard I am experiencing a keyboard, a computer, a chair, vehicles passing on the road, people going around etc. With all these objective experiences I am also experiencing my body, my thoughts and emotions subjectively, means these experiences of body, mind and emotions (heart) are my own, only I can experience them, no one else. All other experiences are common to all of us. So, experience has two sides, objective and subjective. In these two types of experiences, there is a common thing which is they both are momentary. Situations around me are continuously changing and my subjective experiences are also continuously changing. But at the same time there is another factor involved in this whole game of experience, that factor is experiencer of both of these experiences, the Consciousness which is experiencing these both objective and subjective experiences is constant, it is not changing because if the Consciousness was also changing the no experience is possible, as without a constant screen we cannot watch a movie similarly without this constant Consciousness I cannot have any experience at all.
Now I will add something more in the types of experiences, right now I am experiencing the world around me but I do not experience it 24/7, there are times when I do not experience the world at all, which happens in sleep and there are time when I experience the world in a different space time than the current one, which happens in dream. So I can say by my own experience that I keep travelling between space time, which is waking state and dreaming state and no space time, which is deep sleep state. In other words the body which I use to experience the objective world and the subjective experience of the body cannot function continuously, they both have to rest to stay alive or working. But does it mean the no space time experience in deep sleep is also dependent on the condition of the body?
Answer to above question is, no. The very experience of absence of space time can happen without body and it's subjective experience, with body I cannot experience the absence of space time. So, to come to a conclusion I, the Consciousness who is capable of experiencing the absence of space time is not affected by space and time, I am immortal.
Now we will look at the world as a whole. We come to conclusion that the I which experience the waking, dreaming and deep sleep is immortal. The world I am experiencing right now, the keyboard, computer, vehicles on the road, people passing around, my body, mind and emotions, is space and time. All these happenings are happening in space time. But where is space time itself? We experience it so it is not absolute nothing, it is something, but that something has not existence of it's own, because if it had any existence it would have been my permanent experience. Since I am able to travel between space time and no space time, I have to conclude that the space time itself is not a permanent thing, it has also another side which is absence of space time. The space time and absence of space time are happenings which are happening in the Consciousness itself. In other words the world is in I (the I who travels in space time and no space time), I is not in the world.
Now let's come to our basic question, does God exist? After the above discussion the answer to this question is YES, God exists, only God exists, we are mere momentary happenings in the God.