The casual terminology of saying we are Born Again when we're Saved is a misunderstanding of John 3. Doesn't mean I think everyone who uses it understands Salvation incorrectly, it just means we need to clear up some terminology.
Before I explain this view, I want to distance myself from certain others teaching this same thing but tying it into other bad ideas.
Some over emphasize the use of the word "Spirit" in John 3 to support viewing the Resurrection as only Spiritual and not a physical Bodily Resurrection. That is Gnostic Heresy.
And some try to connect their denial of Eternal Security. I don't base my Belief in Eternal Security on the verses about being Born Again, or Born of God, or any of that. That's Calvinism not true Eternal Security. I base it on the verses in John 3 about "Whosoever Believeth on him shall not Perish but have eternal life", it's not Eternal if it can be lost. And other verses showing that even the seemingly proffering Christians who are damned are all those who NEVER knew Him. And how none shall pluck them out of His hand. And 1 Corinthians 3:15 showing that at the Bema Judgment there will be people who's works are burnt up but are still saved.
Since the moment we Believe is the conception not birth, they'll point out that sometimes babies miscarry. A child Begotten of God cannot miscarry. I think the Man-Child of Revelation 12 can represent The Church and individual Believers as much as it does Jesus himself. We are the Body of Christ and also promised to "rule the Nations with a Rod of Iron". Satan wants to prevent the Child from being Born, which is why he accuses us when we Sin. But it is impossible for him to succeed. The Man-Child is then Raptured, same Greek word as in 1 Thessalonians 4, which is when we are Resurrected.
We are already Begotten of God
1 Peter 1:3 says "Blessed be the God and Father of our Lord Jesus Christ, which according to his
abundant mercy hath begotten us again unto a lively hope by the resurrection of
Jesus Christ from the dead". Begotten is a word that refers to conception, not to birth.
1 Peter 1:23 is mistranslated in the KJV "Being born again, not of corruptible seed, but of incorruptible, by the word of
God, which liveth and abideth for ever." The Greek text here does not use the same word used describing the Born Again concept elsewhere, it should read begotten again, Peter's instead using the same word he used in verse 3. The two Greek words are similar but distinct. This is not based on Alexandrian manuscripts, I'm using the Textus Receptus.
We are God's Children already just as a parent considers a baby still in the womb their child already. But Son of God as a technical term applies when we're completely redeemed in the Resurrection, like how it applies to Angels and to Adam before The Fall.
Romans 8:16-21 "The Spirit itself beareth witness with our spirit, that we are the children of
God: And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be
that we suffer with him, that we may be also glorified together. For I reckon that the sufferings of this present time are not worthy to be
compared with the glory which shall be revealed in us. For the earnest expectation of the creature waiteth for the manifestation of the
sons of God. For the creature was made subject to vanity, not willingly, but by reason of him
who hath subjected the same in hope, Because the creature itself also shall be delivered from the bondage of
corruption into the glorious liberty of the children of God."
We are fully the Children of God when we are free from The Curse of Genesis 3, which is what Romans 8 is all about.
James 1:18 "Of his own will begat he us with the word of truth, that we should be a kind of
firstfruits of his creatures." "First Fruits" is a term linked to the Resurrection, that's why Jesus Resurrection was on the Feast of First Fruits.
1 John uses various forms of the same root that the word for born and begat come from, that the Strongs all label one word, and how the KJV renders it can cause confusion.
1 John 3:9 is correct in the KJV, it's abused by those trying to say a Believer cannot Sin. But this same Epistle John explains we Lie if we say we do not Sin.
1 John 4:7 it should read begotten, it's showing how anyone following the Biblical Law of Love is saved and knows God.
1 John 5:1 is also correct. John 5:4 should be Begotten, everyone who's Saved has Overcome the World in once sense according to John. But that can be distinct from Overcoming to the End. 1 John 5:18 is also correct, but what it means is also abused, but it shows the distinction between being Born and Begotten.
In John 3 itself Jesus says that those who are Born Again are those who can see The Kingdom. To say that is true of Believers already takes what he means a lot less literally. When we are Resurrected we will no longer be limited to our current 3 dimensional perception.