You're approaching it the wrong way. The burden is one of seeking, not proof. If you're looking for a sheet of data to convince you from a position you currently hold, I don't imagine I can give you anything to change your mind. One must be searching with all the heart, soul and mind, genuinely searching to see the kingdom of God.
"Biblically God hides Himself to all except to those who by His grace seek him with their whole heart, mind, soul, and strength sincerely and in truth. Not just the mind!!! If we seek Him fully He has promised to meet us on the road. There is no burden of proof, but a burden of seeking, not just with the mind, but with the whole being, a burden which cannot find fulfillment without grace. Grace not just to know, but to follow. Not just to enrich one's life, but to lose it." - from a friend of mine.
"Let them at least learn the nature of the religion they are attacking, before they attack it. If this religion boasted of having a clear vision of God, and of possessing Him plain and unveiled, then to say that nothing we see in the world reveals Him with this degree of clarity would indeed be to attack it. But it says, on the contrary, that man is in darkness and far from God, that He has hidden Himself from man's knowledge, and that the name He has given Himself in the Scriptures is in fact The Hidden God (Is 45:15). Therefore if it seeks to establish these two facts: that God has in the church erected visible signs by which those who sincerely seek Him may recognize Him, and that he has nevertheless so concealed them that He will only be perceived by those who seek Him with all their hearts, what advantage can the attackers gain when, while admitting that they neglect to seek for the truth, they yet cry that nothing reveals it? For the very darkness in which they lie, and for which they blame the Church, establishes one of her two claims, without invalidating the other, and also, far from destroying her doctrine, confirms it" (Blaise Pascal, Pensees, 335).
"Your fountain, Lord, is hidden from the person who does not thirst for You." -Ephrem the Syrian (Faith 32:2-3)
Isaiah 45:15-16
(ESV)
15 Truly, you are a God who hides himself,
O God of Israel, the Savior.