καὶ ὅτι ἀπὸ βρέφους τὰ ἱερὰ γράμματα οἶδας τὰ δυνάμενά σε σοφίσαι εἰς σωτηρίαν διὰ πίστεως τῆς ἐν Χριστῷ Ἰησοῦ
Since βρέφος is used to describe a baby or infant, even one unborn, applying it to Timothy creates some confusion for translators:
And because from thy infancy thou hast known the holy scriptures, which can instruct thee to salvation, by the faith which is in Christ Jesus. (DRA)
and how from childhood you have been acquainted with the sacred writings, which are able to make you wise for salvation through faith in Christ Jesus. (ESV)
The literal translation is "from infancy" as a few translations have, but an infant cannot know, εἴδω, the Scriptures as the other five uses of the word in this letter demonstrate.
It appears Paul has applied the word to Timothy as Peter applied the word to the Jewish Christians of the Diaspora:
So put away all malice and all deceit and hypocrisy and envy and all slander. Like newborn infants, long for the pure spiritual milk, that by it you may grow up into salvation — if indeed you have tasted that the Lord is good. (2 Peter 2:1-3) [ESV]
Peter writes to the "elect exiles of the Dispersion...", somone like Timothy's mother who was a Jewish believer living in Lystra:
Paul came also to Derbe and to Lystra. A disciple was there, named Timothy, the son of a Jewish woman who was a believer, but his father was a Greek. (Acts 16:1)
Peter calls Timothy's mother "a newborn infant." Obviously he is writing to those who have been "born again" not to biological infants:
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 (1 Peter 1:3)
I believe Paul is saying Timothy was raised as a Christian from birth. That is to say, his Jewish mother (and possibly his Greek father) believed in Jesus as The Christ before Timothy was born and so Timothy was raised accordingly. In this particular case, Timothy's knowledge of the Scriptures "from infancy" would carry a double meaning. He was raised in a family where the Scriptures were taught from his natural birth and to the extent infants can learn, Timothy "knew" them. Later, Timothy made the decision to become a Christian and then he immediately knew them as one "born again to a living hope through the resurrection of Jesus Christ."