The essential difference between beliefs based on scientific proof and those based on faith is revelation. So, for example, we believe that the earth travels around the sun because mathematical and astronomical evidence shows that it’s so. But belief in a Supreme Being or divine intelligence behind the universe is clearly beyond the range of physics, and comes into the realm of metaphysics.
For people of faith, the evidence comes by way of revelation. Jesus taught that the deep inner conviction within a person that God is real, doesn’t come primarily through the intellect, but through something far deeper within us – something we call the spirit. That doesn’t mean that it’s intellectually untenable. It just means that we experience it at a deeper level, and then begin to understand it intellectually.