I lean toward baptism as what Jesus was referring to when he said you must be born of water and of the spirit.
If I were to find a reference in ancient literature at the time of Christ that used the phrase "born of water" to refer to natural child birth I might change my mind or see that it could be a possibility. Until then it does not seem logical that Jesus would invent such a phrase and that the disciples would know what he meant.
However we do know that they were knee deep in the subject of baptism in water, and that since the first day they met Jesus it had been part of their daily discussions and religious concepts. They themselves were involved in baptizing people and if it was not a cultural norm to refer to natural birth as "born of water, by water etc" then their first thoughts would be that Jesus was referring to the spiritual significance behind baptism which they preached and focused on at this time.
The amniotic fluid may make
you think of water but I am not so sure that the disciples would think of this. Unless you can find that it was a cultural norm to speak like that.
If anyone has seen evidence in ancient literature from the time of Christ or before where any phrase similar to "born of water" was used to refer to natural birth it would be strong evidence that Jesus might have meant that. Otherwise it would seem that Jesus would know that his disciples would think he was talking about baptism and he would have used another phrase like born of the womb and born of the spirit.
5Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
6This is he that came by water and blood,
even Jesus Christ; not by water only, but by water and blood. And it is the Spirit that beareth witness, because the Spirit is truth.
7For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
8And there are three that bear witness in earth, the spirit, and the water, and the blood: and these three agree in one.