The first premise is wrong so the rest of the Catholic position falls apart.
Man is not saved by works, or which infant water baptism is one, done to someone without their consent.
John 1:10-13 He was in the world, and the world was made through him, yet the world did not know him. He came to his own, and his own people did not receive him. But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
Salvation is by faith, by believing on His name and receiving Him by faith.
An infant cannot exercise that will to choose and nobody can make that decision for them.
....Yet according in the Acts of the Apostles, WHOLE households were baptized, and that included little babies.