How often to we look at a baby and comment something like "he's the spittin' image of his daddy!" And of course, we all got our DNA from our fathers, mothers, and their fathers and mothers going all the way back to God's initial creation of mankind in His own image. So we do carry the image of our Father God in every cell of our bodies.
I find it interesting that we find very few references to God as our Father in the Old Testament. The two references I could find (Isaiah 9 and Psalm 89) have a Messianic context. Where we do find God described as our Father is in the teachings of Jesus and the writings of Paul. We see God as Father in two ways: one is as the Father of the Son, Jesus, and other as His followers as children of God, the Father. In the Sermon on the Mount, (Matthew 5-7) Jesus continually speaks of "your Father...", and tells us to pray to "Our Father...". The God that Jesus describes is not a remote, impersonal power out there somewhere, but a Person, who relates to us as a Father, and whom Jesus also continually calls " My Father."
Paul, in writing to the churches he mentored, begins each of his letters with a reference to "God our Father." This relationship is tenderly described in Romans 8:15: For you have not received a spirit of slavery leading to fear again, but you have received a spirit of adoption as sons by which we cry out, “Abba! Father!”
We see a wide range of fatherly or unfatherly behavior in this world. There are fathers who do a good job of the calling to raise a child "in the way he should go", and some who are missing in action. We can look at God as the source of wisdom for the fathers in our lives; finding the Godly mix of standards and tenderness, and for the strength to carry through on it in good times and not so good times. In the long run, we all have a loving father available: the Psalmist praises God as "A father of the fatherless and a judge for the widows, Is God in His holy habitation."