Yeshua or the writers of the Apostolic Scriptures did not invent the term “born again”. Rather it was a rabbinic term for a Gentile who underwent a formal conversion to Judaism. Part of the conversion ritual involved a full body immersion into a mikvah, i.e. baptism. [See Torah Club Val pages 28-29; and Volume 4 “Noah’s Mikvah] Through the process of conversion and immersion, the Gentile proselyte was regarded as being re-created into an Israelite. In the Talmud, this concept is expressed in tractate Yevamot.
When he comes up after his immersion he is deemed to be an Israelite in all respects. Yevamot 47b.
Rabbi Yose said,” One who has become a proselyte is like a child newly born.” Yevamot 48b.In his book the Waters of Eden, the late Rabbi Aryeh Kaplan, drawing on traditional Jewish thought and sources about the mikvah immersion ritual comments on the born again imagery of the mikvah. Consider the following passages from his book on the subject.
Emerging from the Mikvah is very much like a process of rebirth: Seen in this light, we see that the Mikvah represents the womb. When an individual enters the Mikvah he is re-entering the womb, and when he emerges, he is as if born anew. Thus he attains a completely new status…. When he emerges, he is like one reborn… We therefore see that immersion in the Mikvah represents renewal and rebirth. [Kaplan, 1995, pages 320-323]
“Like one reborn” is a general Talmudic way of speaking about proselytes. The rebirth of Gentiles who passed through the Mikvah was taken literally by the sages. Gentiles born again as Jews were regarded as having no kin. In a legal sense, they were regarded as completely new creatures. Old family ties and relations were considered defunct, as if the convert had actually died and then come back to life as a different person.
Traditional readings of John 3 have always assumed that Yeshua coined the phrase “born again” in His conversion with Nicodemus We have generally taught that Nicodemus was confused because he interpreted the phrase literally. Nicodemus puzzled, “How can a man be born when he is old? He cannot enter second time into his mother’s womb and be born, can he?” (John 3:4) According to our traditional understanding of the passage Nicodemus was baffled by Yeshua’s use of figurative language as if he has never encountered the use of metaphor before.
However, in the rabbinic context, the phrase “born again” was already in use. A born again person was a Gentile who had converted to Judaism under the auspices of the rabbinic ritual. It referred to the symbolic death and rebirth the convert underwent as he passed through the waters of baptism. The immersion into the Mikvah is regarded like re-entering the womb from which the proselyte is reborn as a Jew. “When an individual enters the mikvah, he is re-entering the womb, and when he emerges, he is as if born anew,” Rabbi Kaplan wrote.
When Nicodemus objects and says, “How can a man be born when he is old?” It is not because the figurative language has left him baffled. Rather, he is employing the same metaphorical terminology that Yeshua was using. According to the imagery, Nicodemus was objecting to Yeshua by saying, “I am already Jewish. How can I convert to Judaism?” It is actually a sound objection.
Yeshua goes on to explain, “Amen! Amen! A man must be born of water and spirit!” In other words, Yeshua tells Nicodemus that it is not enough to simply be Jewish. To be ethnically Jewish, or even to be a convert to Judaism via the rabbinic ritual is not adequate for entrance to the kingdom of heaven. A spiritual conversion of the heart is the conversion experience that is really necessary. In essence, Yeshua is warning Nicodemus not to rely on his ethnicity (that is his Jewishness) for salvation. “You need to have a converted heart,” Yeshua tells him.
“Flesh gives birth to flesh,” he says, which is to say, “A Jew gives birth to a Jew, but spirit gives birth to spirit.” It is not adequate to be merely a physical descendant of Abraham, one must also be born of the spirit of God, and that is a spiritual transaction.
This spiritual rebirth is implied by the ambiguity of the word anathon which the New International Version translated as “again” in the phrase term “born again.” The Greek word anathon can also mean “from above.” The one “born again” is born from above. The convert’s rebirth from above, in pharisaic symbolism, was a type of resurrection from the dead. [Daube (1956) “A baptism catechism.” Pages 106-139] Thus, the rebirth imagery was tied closely to the belief in resurrection. To be born again, or born from above, then would mean to be raised from the dead. The novel idea of resurrection from the dead before death is a motif that Yeshua will explore later in John’s Gospel.
Hebrew word play is at work in the master’s saying, “wind blows where it pleases. You hear its sound, but you cannot tell where it comes from or where it is going.” The Hebrew word for “wind”, ruach is the same word used for “spirit.” 
The above material, from Torah Club Vol 1, suggests a further thought, if the idea of being "born again" was so widely understood in the context of the "proselytization" ritual in the first century, could it be that Paul's use of the ideas of becoming a new creation in 2 Cor 5:17 and Gal 2:20 might also be understood as part of proselytization?
 Torah Club Vol 4, FFOZ Publications.