John 3:1-21 describes a conversation between Jesus and Nicodemus (member of the Jewish ruling council) about the importance of being born again.

Jesus indicates that a person has to be born again to enter the Kingdom of God. Nicodemus is skeptical and asks “How can this be?” Jesus does not answer the question but instead scolds Nicodemus (You are Israel’s teacher,” said Jesus, “and do you not understand these things? I tell you the truth, we speak of what we know, and we testify to what we have seen, but still you people do not accept our testimony. I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things?). It is very clear from God’s own words that there were people who were very skeptical of his claims then as they are now!

Verses 18 and 19 clearly states who will be condemned and who will be saved: “Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God’s one and only Son. This is the verdict.” There is nothing in John 3:1-21 to indicate that Jesus wants a personal relationship with any of us. All we have to do is believe in him to be saved.

I disagree with your statement about “his well-documented, perfect and transfigurative death on the cross”. Any fair reading of Matthew, Mark, Luke and John would show the varying accounts of the crucifixion and the resurrection. In addition most Jewish people do not agree with the details of the death on the cross and the Koran (4:157) states that Allah raised Jesus up alive before crucifixion.

There is no evidence outside of scripture for these events.