Question: "When did Jesus know that He was God?"
Answer: The Bible does not clearly state that there was a point at which He knew that He was the second Person of the Trinity. At some point, Jesus fully realized who He was from eternity past, expressing it this way: "Jesus said to them, “Most assuredly, I say to you, before Abraham was, I AM.” (John 8:58). "And now, O Father, glorify Me together with Yourself, with the glory which I had with You before the world was." (John 17:5). But the preincarnate Christ always knew He was the second Person of the Trinity. He made the worlds: "(God) has in these last days spoken to us by His Son, whom He has appointed heir of all things, through whom also He made the worlds" (Hebrews 1:2). Jesus knew from the foundation of the world that He would die for our sins: " Between you and the woman, And between your seed and her Seed; He shall bruise your head, And you shall bruise His heel.” (Genesis 3:15), and "..... the Lamb slain from the foundation of the world" (Revelation 13:8).
While we do not have a clear scripture revealing the thoughts of Jesus as a baby, we can at least discover from Scripture that as a young child He was well aware of His work. Jesus was preparing even as a boy to finish the work His Father sent Him to do. When His parents were concerned about His being missing on a trip to Jerusalem, they found Him in the temple "sitting in the midst of the teachers, both listening to them and asking them questions." (Luke 2:46). When asked why He would disappear and worry them so, He told His parents: “’Why did you seek Me? Did you not know that I must be about My Father’s business?’ But they did not understand the statement which He spoke to them.” (Luke 2:49-50). Joseph and Mary may not have understood, but Jesus certainly did understand at the age of twelve that He was the Son of God and that the Father had foreordained the work He was to do.
After the incident in the temple, we are told "And Jesus increased in wisdom and stature, and in favor with God and men" (Luke 2:52). If at this point in Jesus' experience He knew everything, it would not follow logically that He would need to "increase in wisdom." We know He had to grow physically (in stature), but we must also believe the scripture where our understanding fails us, that is, that He also put Himself voluntarily in a position where He needed to assimilate knowledge as a man. He needed to be truly man. He was always God, but He needed to become in all ways, except for sin, a man as well. In theological terms we refer to this as the hypostatic union. In order for Him to have a legitimate experience of temptation, He needed to limit certain facets of divine advantage. In this He emptied Himself of all His observable physical characteristics of divinity such as described in Revelation: "His head and his hairs were white like wool, as white as snow; and his eyes were as a flame of fire; And his feet like unto fine brass, as if they burned in a furnace; and his voice as the sound of many waters" (Revelation 1:14-15). We know this to be true because Isaiah describes Him in this way: "For He shall grow up before Him as a tender plant, And as a root out of dry ground. He has no form or comeliness; And when we see Him, There is no beauty that we should desire Him. " (Isaiah 53:2).
We can conclude that although the preincarnate Jesus knew from eternity past who He was and what His work in the world was to be, the incarnate Jesus came to that realization at some point in His earthly life. Just what that point was, we cannot know for sure.