By "faith of God" we are referring to an ability or a character in the nature of God. Just as wisdom is a character that enables one say and do wise things, faith is also a character, something that is inherent in the nature of God. This character enables one to be faithful, as he is able to trust and act in accordance with that trust.
Faith as a character is the ability to submit oneself completely and confidently trust in something or someone. Yes, God has faith, He has faith in Himself, He has faith in His ability, and out of that faith comes the confidence that is needed to demonstrate His power. Power and authority can only be exercise through confidence.
Without confidence, words of command become powerless. So when God said, "let there be light", it requires the confidence of faith to fill those words with enough power that would cause light to come out of nothing. God exercises His power by faith. Yes, God also need or use faith, but the faith that He needs is Himself, just as the power that He uses is Himself.
"but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God." (1Cor 1:24).
Christ is the power that God uses, he is also the wisdom of God. We have established that wisdom and faith is a character in the nature of God, and the scripture tell us that Christ is the expression of the nature of God (Heb 1:3). Whenever any aspect of the nature of God is expressed, that is Christ.
"In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made." (John 1:1-2)
"The Lord by wisdom founded the earth; by understanding he established the heavens;" (Pro 3:19).
During creation we see the Word at play, Wisdom was also involved, Faith was required, and Power was used, but all of these things is one person—Christ. So just as the world was created by the word, by the wisdom and by the power, one can also say the world was created by the faith (Christ).
"For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him." (Col 1:16).
Christ is the faith that made the world out of nothing. He is the faith that caused light, plants, animals and all created things to be produced out of nothing. He is the faith that makes a single word of command produce such powerful effect. And now this faith has come to dwell in you.