This is an interesting question in that it expresses something that can be a stumbling block for many people who would like to believe in God but cannot for they don't see why the reality of God would be obscured, should such a being exist. Why would his existence not be blazingly apparent? This is true whether one conceives of divine reality as personal or impersonal or, as must surely be the case, as something that includes but goes beyond both of these human perceptions which may reflect truth to some degree but are still limited.
Q. If God is everywhere why can't we perceive him? I don't mean see him as an object out there, of course, but why can't we at least feel him or sense some kind of spiritual presence?
A. There is an idea that for God to create he had to withdraw himself from part of himself. He is the all. There is nothing other than him. So, in order to create something other than himself (and a creation is necessarily that), he has to make a space in which that can happen. Thus he has to withdraw his presence (figuratively speaking) from a part of reality, the part in which creation may then take place. This is the void or nihil in which creation happens and the universe arises. Now, when God creates he is again present as he must be in his creation because there is nothing apart from him, and if he were not present in anything it would instantly cease to be and go back to the nothingness it was before he willed it into existence. But he is not present in the same way as he was before he withdrew the totality of his being. He is there as the substratum of existence, this is his immanence, but his transcendent being remains outside the creation. This may help explain why, to our currently limited awareness, there is always a feeling of absence. And yet this absence is necessary for us to grow into properly self-conscious individuals. If full awareness of our divine parent were always there, we would never become independent and free which is the point of our creation. We must be alone, or seem to be alone, for that to happen. Only through separation can we reach completion, that is to say, knowledge of completion.
This is part of the answer to your question but I believe there is more to it than the basic mechanics of creation. The Fall, whether seen as a necessary factor in evolution or an error on the part of infant humanity deceived by an anti-spiritual force, is that moment when we cut ourselves off from our divine source. Before then we walked in the presence of God. Afterwards that presence was lost. It was lost because we separated ourselves out from the rest of life. We could no longer sense God's presence because, by identifying ourselves with our selves, we withdrew from him. So it is not that we can't see him because he is not there. Rather we can't see him because we have blinded ourselves.
I agree with the story of how human beings lost their connection to the divine as it is presented in the book of Genesis. So I think the reason this happened was the result of error, though whether that error was in some way intended, never mind foreseen, is not something I want to go into here. What I would say is that self-consciousness, which is an important part of the process that brings a newly created spark of individualised spirit to authentic godhood, could surely have awoken and proceeded on its way without the full descent of the Fall, but we slipped into identification with matter and the concomitant spiritual darkness, sin and illusion because of our disobedience and resistance to truth. We preferred the way of our own will to that of submission to the will of God which only means coordinating our being to truth since God is truth. But we preferred the fluctuating relativism of our own point of view about reality to reality itself because we wanted to possess it instead of be possessed by it. This has reached a critical point today when all traditional restraints (in the form of revealed religion) have been removed and we rely solely on our own knowledge and experience, necessarily always limited, for understanding the world and ourselves. The only way back is through spiritual obedience and openness to truth. But how many of us today are really willing to put aside our prejudices and opinions and submit to truth as it really is, always unfashionable and accessible only to those who are able to become as a child? Which, by the way, does not mean someone who throws aside discrimination and common sense but someone prepared to be humble, accepting and trustful of legitimate authority while, at the same time, retaining proper discernment and responsibility for himself.
Whatever the implications of the Fall there is another reason why we are not given the full revelation of the existence of God so that all doubters would be silenced, and it has to do with spiritual development. Think of the matter like this. If the reality of God were beyond dispute we would all be inspired to become saints, wouldn't we? Our hearts would naturally incline us to goodness and truth in the light of such a revelation. But is that really the case? Unfortunately I don't believe it is. Such is fallen human nature it is by no means certain that outer knowledge would bring about inner change. Change, as in true transformation, must come from within if it is to go all the way down and not just be like a dye that only stains the surface. That is why there is just enough evidence for God to support those who are faithfully looking for him, but not enough to convince those who want to deny his existence. Ultimately the choice is ours which is why it is correctly said that faith is a matter of will rather than intellect. If we turn to God without being compelled to do so because of irrefutable evidence it is because we want to do so which means we are allowing God to be born within us. In a way we are becoming godlike ourselves, or, at least, beginning to. This means that God can, if we continue to cooperate and not arrest the process by the ego trying to take it over, start to effect spiritual change from within. God is like a seed that must be planted deep in the heart itself if it is to grow effectively. He cannot just be grafted on from without. For the whole being to be transformed the process must start from within.
With regard to your question, it is now widely considered that early humanity did have a sense of spiritual presence but it was fairly rudimentary and certainly did not include full participation in divine being. There was no creativity, no love and no real intelligence. It was, if you like, passive not active, instinctive but not fully conscious We had to lose that connection to oneness and know separation in order to regain the awareness of oneness but this time with complete knowledge of ourselves added. This is the journey from pre-lapsarian Adam in the Garden of Eden to the risen Son of God who inherits the Kingdom of Heaven.
And so, to sum up, I would say that there are two reasons for us not being able to perceive the reality of God. One, the legitimate, is that we need to be distanced from the spiritual centre in order to develop a real self-consciousness. This is what you might call the result of a natural evolution. Like the prodigal son we then have to return carrying the fruits of our experiences. But the other reason is self-inflicted, and it is that we have withdrawn ourselves from God by identifying with the separate self. We have rebelled and rejected God. This is the Fall, and it is this we must address in ourselves in order to begin the homeward journey and that, I'm afraid to say, is something we can only do through acceptance of sin and repentance. These are old-fashioned terms I know, but if they have unpleasant connotations for you, ask yourself why. The fact of the matter is that we all have a fallen self, and it is this self that blinds us to the reality of God.
Having written all the above, there is one last point I would like to make. It is this. Why do you assume that we cannot perceive God? Is he not plainly present in the beauty and order of nature and the universe, if you look with unprejudiced eyes? Does he not speak to you through the voice of conscience? And is not the desire for God, a desire that all men have always had, indicative that he is there? For just as there could be no eyes without light so there can be no desire for God if God does not exist.