One can use visible, but not easily debunked, logical chain as method to prove existence of God, especially to a not seasoned mind. Say, woman got raped and questions God's intention. Religious leader explains that God knew of this person's intention ahead of time, and for that reason decreased person's murderous attempts so greatly, that woman actually survived. Thus God saved her life.
Another person got beaten up by his brother, he also has questiones. The answer goes like this: when your brother was a baby, God, knowing of his intentions in a future, threw him into a pot of scolding water, so his right arm got burned and weakened. If God did not do this, your brother could have killed you. So, God saved your life.
For unscrupulous mind it seems almost obvious. While others would ask how come God plays role of only debugger and not creator of the world. Of course, he can be creator as well, but the world mulfunctions in a way computer systems do, so God is busy in ongoing manner fixing mulfunctions of the system he created. The more he fixes, the more reliable the world becomes, the more we pay for it. Not every religious person's favorite set up, I beleave.