Just as an aside, it wasn't miraculous. Biblical miracles, strictly speaking, are (1) physically performed by a human being, (2) physically and visibly witnessed by other human beings, and (3) actions which are counter to God's natural laws of nature. Their purpose is always, primarily, to give divine legitimacy to what the one performing the miracle is about to say or do. The new birth is not something that may be witnessed physically.
The new birth is a spiritual act of redemption by God. John 3:8 The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit."