God is spirit. We cannot see, hear, or touch spirit. Therefore, we cannot see, hear, or touch God - at least not directly. That is why he gave us his Word, the Bible. And that is why we must look at Jesus to see God.
Lots of things cannot be "proven" through the scientific method. Love, for example, cannot be weighed on a scale or poured into a test tube. And yet we know love is as real as anything in this world. People set themselves against tremendous odds, endure tremendous hardships, go tremendous distances - all in the name of love. The greatest example of love, of course, is God's love for us: "God loved the people of this world so much that he gave his only Son, so that everyone who has faith in him will have eternal life and never really die" (John 3:16, CEV).
In addition, while there may be little direct evidence for God's existence, the indirect or circumstantial evidence is formidable. For example: 1) The universe must have had a beginning - and hence a "beginner." 2) Complicated design - i.e., evidence of an intelligent designer - is found throughout all of nature, even down to the DNA within a single cell. 3) Certain moral laws - against murder, rape, stealing, lying, etc. - have been and still are accepted by a large number and variety of cultures around the world (When Skeptics Ask).