I’m surprised that a Bible Christian would ask this question.
4There is one body and one Spirit—just as you were called to one hope when you were called— 5one Lord, one faith, one baptism; 6one God and Father of all, who is over all and through all and in all. (Ephesians 4:4-6)
A second baptism would be not only unbiblical but anti-biblical. You’re not recommending this, are you?
“Believe and be baptized” as you say, is the norm for those who have reached the age of reason. Since the NT was written during a time when most converts were adults (there hadn’t been time for any babies to have been born into Christian homes, yet), the rubric you describe seems valid.
However, as Paul calls baptism the “circumcision of Christ”, we can expect that dutiful Jewish parents who converted to Christianity would have brought their infants into the New Covenant at a tender age just as they had brought them into the old by circumcising them on the eighth day.
Hope this helps. :tiphat: