THERE ARE MYSTERIES you can solve by taking thought. For instance, a murder mystery whose mysteriousness must be dispelled in order for the truth to be known.
There are other mysteries that do not conceal a truth to think your way to, but whose truth is itself the mystery. The mystery of your self, for example. The more you try to fathom it, the more fathomless it is revealed to be. No matter how much of your self you are able to objectify and examine, the quintessential, living part of your self will always elude you, that is, the part that is conducting the examination. Thus you do not solve the mystery, you live the mystery. And you do that not by fully knowing yourself, but by fully being yourself.
To say that God is a mystery is to say that you can never nail him down. Even on Christ the nails proved ultimately ineffective.