We trust God to answer the prayers of his people. By giving new birth, by forgiving sins, by giving his Spirit, by bringing the person to a new life in Christ.
When might this happen? For an adult, it has often happened already before the baptism. In that case the service becomes a public declaration of faith and of prayer for the new disciple. In the case of a child, it may have already begun from birth. It may begin later. Everyone is different.
But what our service assumes is that whether it is a child or an adult, the person will be helped and encouraged to grow in Christ. They will take their place among the believers who gather week by week. They will serve Christ and his body. They will grow in the Holy Spirit.
How do we know if it works? By the fruit of godly living. Do we know how it works? By the grace of God.
Dale