Most Baptists consider infant baptism a Catholic leftover. The Catholics are wrong on baptism. They taught that water baptism regenerated the child and some taught that baptism washed away all your sins to that point in your life. Others taught that baptism was necessary for salvation so they tried to baptize any who were dying without baptism. The Catholics are all wet regarding baptism, immersed in error. (Pardon the puns.) Infant baptism is not a catholic leftover; it is continuation of the Abrahamic covenant - part of the Covenant of Grace. (In Genesis 17 the children did not have faith before they received the covenant sign of circumcision.)
In all sacraments God says something to his people. They proclaim, in brief, there is salvation full and free to be found in Jesus Christ alone. That is God's covenant promise to us. Circumcision, Passover, Baptism, and the Lord's Supper all point to Christ and his salvation. Sacraments are signs that point to Christ and seals that guarantee the truth of the promise. (The promise of salvation is sealed to the person, not the person sealed to salvation.)
In short, baptism is not a sign of our new found faith, but of God's faithfulness to his covenant promise. Personal faith in the Christ signified to me in the sacraments is essential to derive any benefit from them. Still, what the sacraments are does not depend on my faith. Baptism is a sign of salvation that points us to Christ. When you see a sign on the highway that says Burger King, 3 miles ahead; do you stop at that sign and ask for a Whopper? No, you follow the sign's direction and arrive at the restaurant. Baptism points you to Christ. Fly to Christ.
Baptism is a sign of entrance into the covenant community. The reason that faith was necessary before baptism in the NT examples is that the covenant community was being reestablished. It was taken away from the Jews and reconstituted in Christ. Once they entered into the covenant community, baptism belongs to their households as well. There are six examples of household baptisms in Acts.
Adult baptism and infant baptism mean the same thing; a sign that you have entered the covenant community. It is a sign that the promises are yours, and that the covenant sign of baptism belongs to believers and to their children. (Acts 2:39)
Now we must follow up on baptism and respond to what God has said to us; we must improve our baptisms. How do we do that? “We ought, then, seriously and thankfully to consider the nature of our baptism. Christ instituted it to apply the blood that cleanses us from all sin, both to justify and to sanctify us. Our baptism speaks to us of that unqualified acceptance that we have with our God by his declaration of righteousness that we enjoy in justification, and that perfectly in this life. It also speaks to us of the transformative work that goes on in sanctification, a work neither equal in all, nor in this life perfect in any, but growing up to perfection.” (Alan Strange)
Baptism must be blessed by the Holy Spirit and received by faith. We exercise that faith in baptism throughout our Christian life. We must pray for the covenant families that God would bless His sacrament and that covenant children would continually believe what God has told them in baptism.