Regarding regenerate infants within Frame’s paedobaptistic understanding, there would seem to be a weakness regarding what he has already said. Frame recognizes that, considering 1 Peter1:23 and James 1:18, conversion is through the instrument of the word of God.
But I would strongly disagree with Frame on this last point. It seems reasonably clear that neither 1 Peter 1:23 nor James 1:18 refers to a process of spiritual growth but to the inceptional event of the Christian life. In 1 Peter 1 being “born again… through the living and enduring word of God” (v23) seems parallel to “obedience to the truth” (v22) and the “good news that was preached” (v25, also v12). Furthermore, the idea of being “born again” reaches back to v3: “Blessed be the God and Father of our Lord Jesus Christ! According to his great mercy, he has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead.” The most natural way of reading these verses is in reference to that initial regeneration resulting in faith upon hearing the preaching of the gospel. To stretch this to refer to the sanctification process seems unwarranted and a searching for evidence, which Frame links with infant regeneration.
I have recently begun to read Bavinck’s Saved by Grace: The Holy Spirit’s Work in Calling and Regeneration, which a good friend bought for me, so it will be interesting to see how he deals with these things, but for the moment, I feel strongly that if there are passages in Scripture that refer regeneration to the Spirit and the Word, we ought to presume that regeneration does not take place without these things, unless other considerations absolutely demand it.