Note, that Peter, a Jew, was preaching to this Gentile audience when the Holy Spirit fell upon those who were neither circumcised nor baptized. The second part was so that Christian's of all kinds might understand that the outpouring of the Holy Spirit upon a person was not contingent upon that person receiving the outward sign of baptism. Confession of that faith then follows, as does the receiving of the sign of inclusion in God's covenant family. We make a grave error when we assume that the sign of baptism primarily signifies a person's coming to faith or the coming of the Holy Spirit upon him. This is not the purpose of the sign.
Baptism is a sign of inclusion in the covenant relationship, both for infants and adults.
Cornelius and his household that day had been given the outpouring of the Holy Spirit. They were filled with the Spirit even before their public confession, and even before receiving the sign of baptism. Therefore remember, that formerly you, the Gentiles in the flesh, who are called 'Uncircumcision' by the so-called 'Circumcision,' remember that you were at that time separate from Christ, excluded from the commonwealth of Israel, and strangers to the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who formerly were far off have been brought near by the blood of Christ. That is the purpose of the sign of baptism - to mark inclusion in God's covenant promises in Christ.