Please consider Jn. 1:12, for in this very Passage is summed up what you and I both have been discussing.  As such look at the ‘aorists’ tenses, and the final present tense (BELIEVING), in this verse respecting God’s Pre-Ordained Plan of Action for the New Birth. 

John 1:12 (KJV)
12 But as many as
received him, to them gave he power to become the sons of God, even to them that believe on his name:

Therefore, with respect to the above, this verse is talking about the New Birth, BECOMING (ginomai G1096 - to come into existence) a Son of God.  As such, SON-SHIP with God has a BEGINNING moment in time, hence New Birth. 

To this end, 3 critical steps are revealed in this Passage – 1:) Man Believes/Receives; 2:) Jesus/God Grants His Saving POWER; 3) Man BECOMES the Son of God. 

Meanwhile, what is being implied by Jn. 1:13, which follows, is the ORIGIN of the NEW BIRTH Concept itself.  

John 1:13 (KJV)
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

The burden of thought in Jn. 1:13, which MUST AGREE with the grammatical language of Jn. 1:12,  is that the ORIGIN of the Plan of the New Birth is of the sovereignty of God, Spiritual, and from Heaven above, and that it does not derive its origin from the Abrahamic descent of Bloodline, nor of the FLESH of any other living thing, nor of the WILL (wishes/decrees/desires) of the created Man.  

It is ENTIRELY a CREATIVE PLAN/Instrument and ACTION of God…The New Birth FOLLOWS a Pre-Ordained method of application and logical SEQUENTIAL ORDER.  Hence, Jn. 1:12 – BELIEVE/Receive and be GIVEN the POWER of the NEW BIRTH. 

We simply cannot dismiss the clear language of Jn. 1:12 respective of Jn. 1:13 – they must AGREE, and grammatically Jn. 1:13 does not take precedence over Jn. 1:12.  The grammar and language of Jn. 1:12 does not allow for the GIVING of His POWER, and then and only then, the RECEIVING of HIM…that is entirely backwards. 

Going forward, why is Jn. 1:12-13 so important here? 

1 Cor. 2:14 and Rom. 3:9-20 makes it perfectly clear that natural man (FLESH) BY the Deeds/Works of the LAW…CANNOT ‘effect’ to his SAVING.  Thus, is was this condemning LAW (the law by design has no mercy and only reveals and illuminates man’s Sin) that passed the sentence of DEATH upon ALL mankind due to the original SIN of just ONE man.  Thus, DEATH became AUTOMATICLY inherited to ALL who would ever be born.  Hence, 1 Cor. 2:14 and Rom. 3:9-18 came into its reality.  

Romans 5:12 (KJV)
12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon
all men, for that all have sinned:

As such, Paul reveals an EXACT comparative Parallel – two trains going in opposite directions, in Rom. 5:18, ONE man Adam brought Death to ALL mankind, while ONE man Jesus, brought Life to ALL mankind.   

 Romans 5:18 (KJV)
18 Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon
all men unto justification of life.

It is imperative, that we understand that in the two above comparative parallel Passages that the word ALL, does not mean a PARTIAL Dispensation of God’s Grace to only the ELECT, but to ALL mankind.  Therefore, if the POWER of the original SIN was PASSED equally upon and covered ALL mankind alike, Paul reveals by absolute necessity must the POWER of the Cross, equally PASS upon ALL mankind.  Otherwise the POWER of SIN and DEATH IS greater than the POWER of the Blood of Jesus, and His Cross of LIFE. 

To reiterate then, the two Passages are intended to be understood as diametric comparative parallels. 

However, it must be noted, that unlike the Death which is by NATURE of Adam’s original Sin, which is automatically passed upon ALL men – just by the mere fact of their being born, the LIFE in Jesus is NOT an automatic institution.  While this SAVING LIFE was indeed COMPLETED and ESTABLISHED at the Cross, for ALL mankind, unlike SIN and DEATH, it is NOT automatically inherited by NATURAL birth, and the fact of simply being born.  Otherwise there would be no need for the New Birth, just like SIN and the SINNER, men would NATURALLY be born into LIFE and RIGHTEOUS, with each automatically inheriting the LIFE established by the Blood of the Cross.  

As such, Paul reveals how this process of RECEIVING this New LIFE - NOW works for BOTH the Jew and the Gentile, which was even attested to and witnessed by both the Law (those things of the Mosaic Law that symbolized Jesus) and the Prophets. 

Romans 3:21 (KJV)
21 But
now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;

Romans 3:22 (KJV)
22 Even
the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:

Here is the summation, we BELIEVE in Jesus, He/God GRANTS His SAVING POWER, and we BECOME the Sons of God – New Birth. 

How do we ACCESS the SAVING GRACE of God (Eph. 2:8) - it is found in Rom. 5:2...

Romans 5:2 (KJV)
2 By whom also we have
access by faith into this grace wherein we stand, and rejoice in hope of the glory of God.

PLEASE note, if a man can BELIEVE in Allah, if a man can believe in Buddha, and if men in India can believe in over 300 million other pagan gods, and if a man can believe in a god made of wood or stone, and last but not least, if a man can even believe in UFO’s, it only stands to reason, that a man can most certainly BELIEVE in the GOD man Jesus, just ENOUGH to RECEIVE the POWER of God, to BECOME the adopted Son(s) of God hence, the New Birth.