So since John 3:5 makes it an absolute imperative that one be baptized of water and the Spirit, and Rome holds that this water refers to baptism (though i am not aware if she infallibly defines this verse or 1Pt. 321 as teaching that), then you must hold that one must be baptized in order to be born again. Correct? It must be to be consistent.
But that is refuted by Scripture, (Acts 10:38-43; 15:7-9) and the Lord in Jn. 3 is interacting the natural man's understanding, that of Nicodemus, that "born again" referred to a physical birth, and thus the "water" aspect is added, as one must have two births, and water brings forth life in Gn. 1:20. And which is consistent with John, who contrasts the physical and the spiritual, with the physical never gaining eternal life, except faith in the atonement, and who goes back to the "beginning" often.
To me from my understanding, baptism is something one does as an adult as a public showing of your obedience to Jesus. It’s a public affirmation of your faith in him.
I have never seen any scripture indicating that babies were baptized.