Regeneration IS synonymous with other phrases in scripture:
born again/born from above/new birth; new creation; made alive/quickened
Let us speak of these first:
JI Packer states of the New Birth:
The use of the figure of new birth to describe this change ... The regenerate man has forever ceased to be the man he was; his old life is over and a new life has begun; he is a new creature in Christ, buried with him out of reach of condemnation and raised with him into a new life of righteousness..
Packers phrasing here is entirely applicable since being born means you are born into a family. Your birth establishes you are now apart of and in the family and thus have innately within you, aspects of your family, specifically in this case, your Father.
Now in order to be apart of God's family two things just transpire.
1. you must be born again, cause you do not have your Fathers nature
2. for #1 to be come to pass you must be made new; a new creation
Scripture declares that we (believers) are a new creation/creature, old things have passed away (no longer there) behold all things have been made again, new (without stain or taint). However, there is a modifier here.. 'in Christ'. You can not be a new creation without being in Christ Jesus. but we will come back to this and for now just assume it doesn't say "in Christ".
So.. in order to be in God's family, thus able to call him Father, we must have within us a new nature. In order to have a new nature the old nature must be removed and a new one placed within us that corresponds to the Fathers and therefore placing us IN Him. Ergo - set apart from the other or sanctified
Thus, according to scripture, in order to have no stain or taint (regarding sin) before God, we must be justified before Him. If we are not justified before him, we are still tainted and stained and not a new creature. If we are not a new creature (having a new nature) then we have no access to the family of God, therefore we have never been born again.
Another interesting point about being born again or the new birth is that it does indeed speak to the fact that spiritually, they are made alive. But unless you have been born or birthed into the family of God, you are not alive unto Him. Scripture tells us that 'life' or spiritual life ONLY comes through those who are IN Christ Jesus. They are 'in' and therefore one or in union with Him. Rom 6:11 states we are alive unto God through Jesus Christ; 1 Cor 15:22 states that "even so IN CHRIST shall all be MADE alive; Eph 2:5 quickened/made alive us WITH Christ (we are alive because He is alive - He in us and us in Him, who is life) You can not have life apart from Christ Jesus.
YET, one can not be unified in/with Christ, while still in sin, still tainted and stained. He who is thrice holy, will not unite Himself into one being with those who have not been cleansed.
Thus to be born again, into the family of God (sanctification) you must become a new creature (justification).. that you might be IN Christ and thus of the family of God. We find in Titus 3:5 this same compelling statement regarding regeneration.. that it is the work of justification and sanctification.
Titus 3:5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;
NLT states it this way:
He saved us, not because of the good things we did, but because of his mercy. He washed away our sins and gave us a new life through the Holy Spirit.*
Thus salvation and regeneration as seen in this passage as being conceptually synonymous.. we are saved through the work of regeneration.. and regeneration establishes why we are saved.
And in understanding salvation, we note that you can not be saved apart from being justified and sanctified. And you are not a child of God until you are saved, being placed into Christ and making you apart of family of God, whereby God Himself comes to indwell and become unified with the believer. Eternal life is knowing God the Father, and His Son, whom He sent. What is also intriguing is that all of these things happen at salvation, but none of them transpire prior to exercising faith. And therefore I believe, according to scripture, you can not be regenerate (which MUST include justification and sanctification and the infilling of the Holy Spirit) before faith.
WHY?
It is 'by faith' we are justified (Rom 3:28)
It is 'by faith' we are sanctified (Acts 26:18,)
It is 'by faith' we are made righteous (or in union with God) (Rom 3:22, Rom 4:5)
It is 'by faith' the propitiation (substituationary death) is applied to man (Rom 3:25)
It is 'by faith' we receive (obtain) the indwelling Holy Spirit (Gal 3:14)