Agreed, and the "source" here is...Isaac.
Which is referring to the lineage in the flesh and is not a contrast between being born of the Spirit and being born of the flesh.
Note that in view are the "children of promise:" the primary mistake those who believe men were born again before Pentecost make is they impose fulfillment of the promise prior to it's being bestowed.
While the Spirit of God certainly ministered to, in, and through men prior to Pentecost, what we can say for certain is that the Ministry of the Spirit of God in the capacity of Comforter can be seen to begin at Pentecost, at which time the eternal indwelling of God began. It is a certainty that not one of the disciples were Baptized with the Holy Ghost until after Christ ascended:
Acts 1:4-8
King James Version (KJV)
4 And, being assembled together with them, commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, saith he, ye have heard of me.
5 For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence.
6 When they therefore were come together, they asked of him, saying, Lord, wilt thou at this time restore again the kingdom to Israel?
7 And he said unto them, It is not for you to know the times or the seasons, which the Father hath put in his own power.
8 But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.
It is also a certainty that being born again requires faith in Christ, which while many (including the disciples of Christ Himself who ministered under the power of the Holy Spirit) believed in Christ in His earthly Ministry, did not understand Christ as Savior. Peter stood in direct opposition to the Gospel as seen here:
Matthew 16:21-23
King James Version (KJV)
21 From that time forth began Jesus to shew unto his disciples, how that he must go unto Jerusalem, and suffer many things of the elders and chief priests and scribes, and be killed, and be raised again the third day.
22 Then Peter took him, and began to rebuke him, saying, Be it far from thee, Lord: this shall not be unto thee.
23 But he turned, and said unto Peter, Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men.
We see Peter's fleshly mid at work when Peter takes up the sword in the Garden...in an attempt to thwart the very thing that Christ came to do.
If that is not enough, we see Peter, when the Lord is taken, deny that he even knew Christ.
Born again believer?
Not even close.
Again, the promise cannot be imposed into an Old Testament economy.
John 1:11-13
King James Version (KJV)
11 He came unto his own, and his own received him not.
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:
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
John will again refer to the New Birth and how it is accomplished:
1 John 5:1-5
King James Version (KJV)
1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
2 By this we know that we love the children of God, when we love God, and keep his commandments.
3 For this is the love of God, that we keep his commandments: and his commandments are not grievous.
4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
5 Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
Prior to Pentecost no man had entered into the New Covenant. No man was Baptized with the Holy Spirit. It was not until the Spirit of God began taking up permanent residence in believers, who specifically believe on Christ, that the promise and promises of God were fulfilled. One member mentioned that the Old Testament Saints were not perfected until after their deaths, and we see that here:
Hebrews 12:22-23
King James Version (KJV)
22 But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels,
23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect,
Again we consider the children of promise through Isaac and those born of the flesh, the premise of this entire treatment of the New Birth and it's imposition into an Old Testament Economy:
Hebrews 11:13
King James Version (KJV)
13 These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth.
Hebrews 11:39-40
King James Version (KJV)
39 And these all, having obtained a good report through faith, received not the promise:
40 God having provided some better thing for us, that they without us should not be made perfect.
Now let's look at the Lord's statement again:
Acts 1:4-5
King James Version (KJV)
4 And, being assembled together with them, commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, saith he, ye have heard of me.
5 For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence.
Where is the teaching He refers to found?
John 14:16-17
King James Version (KJV)
16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
Shall we, as did King David...plead with God not to take away His Spirit from us? Do we not understand that the indwelling of God in salvation in Christ is eternal?
The promise of the Spirit of God is just that, a promise...until it is bestoed and becomes a reality:
Ezekiel 36:22-27
King James Version (KJV)
22 Therefore say unto the house of Israel, thus saith the Lord God; I do not this for your sakes, O house of Israel, but for mine holy name's sake, which ye have profaned among the heathen, whither ye went.
23 And I will sanctify my great name, which was profaned among the heathen, which ye have profaned in the midst of them; and the heathen shall know that I am the Lord, saith the Lord God, when I shall be sanctified in you before their eyes.
24 For I will take you from among the heathen, and gather you out of all countries, and will bring you into your own land.
25 Then will I sprinkle clean water upon you, and ye shall be clean: from all your filthiness, and from all your idols, will I cleanse you.
26 A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
27 And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them.
Christ reiterates this promise and John 14 and 16 inform us greatly about this coming fulfillment, which took place after the Cross and after Pentecost. One cannot be considered born again apart from the indwelling of God, and we can certainly make a distinction between the promised ministry of the Holy Spirit after Christ's Ascension and before. Shall we view the disciples' temporal expectation...
Acts 1:6
King James Version (KJV)
6 When they therefore were come together, they asked of him, saying, Lord, wilt thou at this time restore again the kingdom to Israel?
...as indicative of born again believers who understand Christ's death, burial, and resurrection?
Not at all.
The promise of the Spirit in the New Covenant fulfillment came when the New Covenant was established. Gentile Inclusion was a mystery prior to New Testament teaching following Pentecost, but that is precisely what took place when Christ began building His Church. Not one Old Testament Saint can be said to have received the promise or promises, for they were not made perfect (complete), which could only occur after Christ had paid the penalty for sin for those that would believe specifically on Him for salvation, thus overcoming the world through Christ.
God bless.