In theological discussion, it is important to make a difference between examples and illustrations. Examples qualify as evidences and proofs of a subject; however, illustrations are not proofs; they only help understand (throw light upon, illustrate) an idea or concept.
Thus, there are no examples of God's existence except God Himself. There is also no example of the Trinity except the Trinity. We can find some illustrations that help us understand these in some way, but the illustrations are not to be regarded as exemplary proofs (that is, to argue that since the illustration is possible, therefore, the doctrine is also possible).
In such discussions, one may turn to rational proofs or/and scriptural proofs for asserting a particular doctrine.