The new birth is only given to those who hear and believe the Gospel, Galatians 3:2.
Since you don't believe the Gospel you have not been born again, Romans 10:17.
The correct order is first being Born of God, then as a consequence are made able to spiritually hear God's Words.
John 8:43, 47
43 Why do ye not understand my speech? even because ye cannot hear my word. 47 He that is of God heareth God's words: ye therefore hear them not, because ye are not of God.
Scripture is clear that the natural man can't believe on Christ because his carnal mind is enmity against God Rom. 8:7-8.
His own faith is worthless, unprofitable.
1 Cor. 2:14
But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
Rom. 3:11-12
11 There is none that understandeth, there is none that seeketh after God. 12 They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
The only Faith that pleases God is a fruit of the Spirit given in New Birth Gal. 5:22.
Rom. 8:9
But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you.