For logical proofs of God, see Aristotle, Avicenna (derived from Aristotle) and Aquinas (derived from Aristotle through Avicenna). Those are objective arguments, ie, no faith required. No belief required. They have been analyzed innumerable times over the millennia by brilliant minds. Some of the arguments have been found to be weak by many analysts. Whole dissertations have been written in examination of, defense, of, apology for, criticism of, etc.

There is a huge, rich literature out there.

Google is your friend.
Aristotle: Http://www.abu.nb.ca/Courses/GrPhil/PhilRel/Aristotle.htm
Avicenna: http://www.iep.utm.edu/a/avicenna.htm
Aquinas: http://www.fordham.edu/halsall/source/aquinas3.html