if you want to believe infant baptisms saves people go ahead, but to say a person can give salvation to another is ridiculous, the apostles were to teach all nations and yes baptizing them- scripturally by immersion at an age of understanding after they called on Jesus to save them.
Acts 2:41-Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
salvation always comes before baptism, baptism is a public testimony of what has taken place in a persons heart.
It wasn't an "or" condition. And it wasn't a "then" condition either. Both were necessary.
Jesus baptized the entire house of Cornelius. Read the Acts of the Apostles. Did it ever occur to you there were children in his house?