Hi Friend of.
The answer is after, and probably much more "after" than you think. It's used twice, once in Titus 3:5 and once in Matthew 19:28. In the latter, we have: "You who have followed Me, in the regeneration (παλιγγενεσίᾳ), when the Son of man shall sit in the throne of his glory, you also shall sit upon twelve thrones judging the twelve tribes of Israel." This is an obvious reference to His return, when the saints shall receive their glorified bodies. Thus physical regeneration is in view here.
In Titus 3:5 we have, "4 But after that the kindness and love of God our Saviour toward man appeared, 5 He saved us, not by works of righteousness which we have done but according to his mercy, through the washing of regeneration (παλιγγενεσίας), and through the renewing of the Holy Spirit; 6 which He shed upon us abundantly through Jesus Christ our Saviour." (Titus 3:4-6).
According to Paul's theology, water baptism followed by the baptism in the Holy Spirit represented resurrection unto newness of life spiritually. But it was ultimately a representation of the resurrection from the dead, i.e the actual regeneration, that will take place at Christ's return. That's how these two verses go together. But again, technically the spiritual experience was not complete unless it was accompanied by the baptism in the Holy Spirit. Those who only receive water baptism in today's Christianity are short-circuiting the steps described in the New Testament. They are saved by believing, but they have not yet "received" as described in Acts 8:14-17. Thus, the "renewing of the Holy Ghost" that Paul referred to in Titus 3:5 was to the baptism in the Holy Spirit, which is what the apostles were sent to bestow upon the Samaritans through laying on of hands, for as of yet they had only believed.
In short, if you are asking when believers become regenerated in the Spirit, it happens when they are baptized in the Holy Spirit. But ultimately this only represents the true regeneration, which will take place at the return of Christ, as per Matthew 19:28.