I would expect that he had known that Jesus was his cousin.
That doesn’t mean by default that he knew that Jesus was THE Lamb of God who takes away the sins of the world.
So he knows that Jesus is his cousin, then did they grow up together? Would John have watched Jesus grow strong from grace to grace? Didn’t John notice the grace of God upon Jesus?
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And the child grew and became strong; he was filled with wisdom, and the grace of God was on him.
http://biblehub.com/luke/2-40.htm
And Jesus grew in wisdom and stature, and in favor with God and man.
http://biblehub.com/luke/2-52.htm
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http://www.jewishencyclopedia.com/articles/7689-high-priest
The High Priest is critical to Israel, but Jesus arrived in apostate Israel. Prior to Jesus with who did the Jews work out their salvation? Who is John the Baptist?