To help you answer your question, it is first of all important to point out that Jesus never actually refers to himself as God. He is referred to as the "Son of God" several times—for example, in Luke 4:41, when the demons declare that Jesus is "the Son of God." However, Jesus never explicitly refers to himself as God; he only ever implies it, like when he says "I and my Father are one" in John 10:30.
However, irrespective of the fact whether Jesus saw himself as God or not, you can most certainly argue that the Bible suggests that Jesus had some knowledge of the world that was at least inspired and enlightened. From the human side of things, Jesus was well aware of suffering. For example, you could mention the fact that he was always trying to help those who were rejected by society, such as people suffering from leprosy or the tax collector. Jesus feels sorry for these people and doesn't mind engaging with them, despite the fact that society looks down upon them. You could argue that this is also a sign of his godly, or inspired, knowledge: Jesus knows that God is an all-loving God, the God of all people, regardless of who they are. Jesus spends time with sinners, as he knows that this is what God does and what God wants him to do. So in answer to your question, whilst the Bible never tells us explicitly that Jesus actually knew that he was God, he definitely acted in a way that represented God's will more than any other human being at the time.