As a devout theist, it feels somewhat heretical to say this, but, there is no proof of God’s existence. What I mean by that is that for all of the evidence of God’s existence, even taken together, it is not sufficient to incontrovertibly prove, once and for all, to all the world that God exists. There have been individuals to whom God has proven his existence, but for most human beings, if we choose to believe in God, there is an element of faith required to continue that belief.
I suspect this proposition is obvious to many who don’t believe in God, while some believers may resist it being stated this way. However, this is actually a very important point in LDS theology for three reasons.
First, we believe that one of the primary purposes of this life is to prove our character by how we act when out of God’s presence. Because the nature of God allows him to know our every move, the only way we could achieve the required independence was to be put into a situation where we could believe God was not there.
Second, in a world where all will inevitably sin, we will be judged with respect to our knowledge and understanding of what is right. So, it is a mercy to withhold this knowledge from those who would be condemned by it.
Third, the process of gaining faith is also central to our purpose in life. “The aim of education should be to teach us rather how to think, than what to think.” The same is true for our spiritual education. Learning to use faith in order to gain understanding and to grow as an individual is key to progression. Having the central tenet of religion be unknowable except through faith demonstrates the central importance of faith.
Ultimately, all of these points boil down to something central to what we believe is the purpose of life. We are here not by random chance or for God’s amusement. We were sent from God’s presence to prove our character and improve our minds. The final judgment will not be based on an arbitrary checklist, but rather on the person we have become through our life on this planet. For those who have chosen not to believe, God will use the same criteria, and has structured His intervention on this planet to give us the best opportunity He could give.