Q: Could Nicodemus be born again when Jesus had not died yet?  

: No. For Nicodemus and the Jews to be “born again” meant that they had to be brought into the new covenant, as the old covenant under which they had been God’s chosen people was about to be done away with and become obsolete. That of course also meant that they needed to accept the mediator of the new covenant, Jesus Christ. (Jer. 31:31-34; Heb. 8:6-13; 9:14-22) The new covenant became operative on the day of Pentecost, with the outpouring of the holy spirit upon the 120 disciples. That was fifty days after Jesus’ resurrection on Nisan 16. (Acts 1:14-15; 2:1-4; Matt. 20:17-18) At that time God’s new nation, concerning which Isaiah had prophesied, came into existence, when Zion gave “birth to her sons.” (Isaiah 66:8; 1 Peter 2:5-10)

The “born again” that Jesus spoke of in his conversation with Nicodemus, is not to be confused with today’s born again doctrine that has become synonymous with a spiritual resurrection, or rebirth, which was preached by some Greek disciples even back in Paul’s day, and concerning which Paul wrote to Timothy: “But shun empty speeches that violate what is holy; for they will advance to more and more ungodliness, and their word will spread like gangrene. Hymenaeus and Philetus are of that number. These very men have deviated from the truth, saying that the resurrection has already occurred; and they are subverting the faith of some.” (2 Tim. 2:15-18; 1 Cor. 15:12-19)

To most people the concept of being “born again” has become “a Protestant term for spiritual rebirth and salvation.” (Wikipedia, “Born Again”) But this is not the “born again” that became necessary for Nicodemus and the Jews as a nation that Jesus spoke of, but which Nicodemus failed to understand at that time. (John 3:1-7; 14:25-26) —
For a more detailed discussion on this subject, please see “Born Again—What Did Jesus Mean?