Was there a time when Jesus Christ did not exist?
This question can be looked at prior to the cross or at the cross when sin seperated him from God the Father, so lets start at the cross when Christ died, and then look at scripture before He was made flesh.....
The Death of Jesus
45From the sixth hour until the ninth hour darkness came over all the land. 46About the ninth hour Jesus cried out in a loud voice, "Eloi, Eloi,[c] lama sabachthani?"—which means, "My God, my God, why have you forsaken me?"[d]
47When some of those standing there heard this, they said, "He's calling Elijah."
48Immediately one of them ran and got a sponge. He filled it with wine vinegar, put it on a stick, and offered it to Jesus to drink. 49The rest said, "Now leave him alone. Let's see if Elijah comes to save him."
50And when Jesus had cried out again in a loud voice, he gave up his spirit.
Did Christ die the same as man and know nothing in the sleep of death....