We could look at a number of Pauline texts about baptism (e.g. Ephesians 4:5, 1 Corinthians 10:2; 12:13; 15:29, Galatians 3:27 etc.)
But I want to focus on two texts in particular which I think capture the heart of what is happening in baptism:
“Or don’t you know that all of us who were baptized into Christ Jesus were baptized into his death? We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life.” Romans 6:3-4
“In him you were also circumcised with a circumcision not performed by human hands. Your whole self ruled by the flesh was put off when you were circumcised by Christ, having been buried with him in baptism, in which you were also raised with him through your faith in the working of God, who raised him from the dead.” Colossians 2:11-12
If we take these two texts as paradigmatic for what baptism is we see that baptism is a symbol showing that a Christian undergoing baptism has died and risen with Christ and now has new life. We know that a person has only truly died and been risen with Christ when they have faith in Jesus and so if baptism is a reflection of this fact why then would we baptise someone who has not yet come to faith in Jesus.
These texts in particular should cause a person who baptises infants to rethink their position. So as we have seen in the Gospels and Acts, baptism is to be conferred on those who have made a profession of faith and therefore the Bible supports believers baptism and not infant baptism.