Can only born-again Christians believe with all certainty that Jesus rose from the dead?

Yes, Romans 12:2 speaks of having a Transformed mind meaning in the Greek is Metamorphosis, also 1Cr 2:10,11 But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God.