My question is about First Baptism. Does it really forgive sins and how?
There is no “first” baptism because there is no second baptism. There is only one baptism (Ephesians 4:5).
Baptism forgives Original Sin and all actual sins of the baptized person.
“Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit” (Acts 2:38)
“And now why do you wait? Rise and be baptized, and wash away your sins, calling on his name” (Acts 22:16)
“Baptism . . . now saves you, not as a removal of dirt from the body but as an appeal to God for a clear conscience, through the resurrection of Jesus Christ” (1 Pet. 3:21)
Baptism is a sacrament. Sacraments are signs through which God truly and really acts and imparts grace to the recipient.
Catechism of the Catholic Church:
1131 The sacraments are efficacious signs of grace, instituted by Christ and entrusted to the Church, by which divine life is dispensed to us. the visible rites by which the sacraments are celebrated signify and make present the graces proper to each sacrament. They bear fruit in those who receive them with the required dispositions.