<"We can't know who Jesus was.">

Not by unaided human inquiry, no. Down through the millennia we are all asked by Jesus of Nazareth: “Who do you say I am?” 

Mohammed certainly arrived at some creative answers to this "tantalizing question" after due deliberation. Saint Peter, on the other hand, was inspired by the Holy Spirit to answer: “You are the Messiah, the Son of the living God."

It's not a "tantalizing question" answerable through human effort, reason, intellect or study - alone. Faith is an unmerited gift of God, received by accepting and using God's grace to deepen one's understanding.