John 3:3
"Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God."
When were you first born? In the natural. Through your mothers "natural" womb.
John 3:4
"Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother's womb, and be born?"
Jesus reply?
"Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God."
And the VERY NEXT scripture?
John 3:6
"That which is born of the flesh is flesh; and that which is born of the Spirit is spirit."
So, would not "natural" birth be of the "flesh? I see nothing of baptism anywhere near these verses, ¯\_(ツ)_/¯
A few more verses Jesus says,
John 3:12
"If I have told you earthly things, (which He did...born of flesh?) and ye believe not, how shall ye believe, if I tell you of heavenly things?"
(Born of The Spirit)
He spoke of natural, birth. "born of water and THEN born of Spirit...? Flesh/Spirit...I see nothing about baptism.
These verses have always had me wondering and, not saying that I'm correct but, I really do not think it is about the water baptism of John.
This is where I have landed so far and...right or wrong, He will reveal it to me.
Love you bro!!! 
Indeed you are correct especially when we break down the passage with its contrasts and comparisons.
John 3:3 Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.”
4 “How can someone be born when they are old?” Nicodemus asked. “Surely they cannot enter a second time into their mother’s womb to be born!”
5 Jesus answered, “Very truly I tell you, no one can enter the kingdom of God unless they are born of water and the Spirit. 6 Flesh gives birth to flesh, but the Spirit gives birth to spirit. 7 You should not be surprised at my saying, ‘You must be born again.’ 8 The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit.”
9 “How can this be?” Nicodemus asked.
10 “You are Israel’s teacher,” said Jesus, “and do you not understand these things?
So lets go through this point by point.
1- to enter the kingdom of God a person must be born again( a 2nd time)
2- flesh gives birth to flesh ( 1st birth )
3- the Spirit gives birth to spirit( 2nd birth )
4- the wind(spirit) blows wherever IT pleases
5- we hear the sound of the wind but do not know where it is coming from or going to
6- the same with the Spirit( we see its effects but not its coming or going)
7- the spirit is the same as the wind- it does as it pleases and we see its effects in both the natural(wind) and supernatural ( spirit)
8- nowhere in this passage does it say that a man chooses to be born again
9- the new birth is compared to the physical birth just as the wind is compared to the spirits work
10- in both cases of birth God is the Active One and the one who is birthed is passive in the process.
conclusion: just as flesh gives birth to flesh( 1st birth as a person) so to does the Spirit give birth to the spirit(the new birth- born again)
There can be no other reading into the text but what has been outlined in the 10 points. Those 10 points are directly from the text.
Regeneration-born again has to do with the wind in the context and parallels the new birth in that process. The serpent illustration is not being born again and Jesus is teaching something else than the new birth afterwards. He is explaining why He was sent into the world after His teaching on the new birth. The serpent illustration being lifted up has to do with Jesus death on the cross when He paid the penalty for sin. 3:14-15
The topic of the OP is specifically the New Birth, Born Again of the Spirit which is compared to the Wind and how it operates.
Do you control or have any influence over the wind ?
Can you call the wind ?
Neither can a person call Gods Spirit in the new birth as its an Act of GOD. See John 1:13. Born again by God.
The PARALLELS and CONTRASTS Jesus makes in the passage are the following 10 off the top of my head reading through the passage :
1- the 2 births
2- the wind and the spirit
3- flesh and the spirit
4- water and spirit
5- earthly and heavenly things
6- effects of both the wind and spirit
7- the seen with the unseen
8- the physical with the supernatural
9- knowing and not knowing, understanding and not understanding
10- entering the kingdom and not entering the kingdom
hope this helps !!!