It is my understanding, from watching videos of Presbyterian Teachers, is that Reformed Theology is Covenant Theology. Infant Baptism is not baptismal regeneration, but enters the child into the new covenant/visible church. But the child still has to come to faith in order to be “born again”.
Edit to add. Actually, I have it backwards, the child comes faith when they are born again. Faith doesn’t cause them to be born again, being born again causes them to have faith.
Perhaps any Presbyterians/Reformed reading this could elaborate.
it to me is a marbled mess. One is clear, Calvin did not hold to the Catholic view, or the view that was practiced ? Yet he comes very close apparently in some writings while clarifying in others. So i don’t want to step on any reformed opinions.
In article here Calvin may indeed say infants are born again, and like Catholics, agree to a sort of confirmation at age of reasoning, If the child departs he does not say he never was a child of God but infers they simply walked away from what they had, key word had( not a double election predestination). I was surprised because he says baptism and circumcision are same for there respective covenants. To me i said good in the respect that he kind of was saying OT saints were regenerated/born again.
“These passages make it obvious to Calvin, that circumcision is the sign of mortification, and that Israel has been chosen as the people of God out of all the nations of the earth(Deut.10:15; Inst.4, 16, 3). As Abraham commands them[the people of Israel] to be circumcised, so Moses declares that they ought to be circumcised in heart, “explaining the true meaning of this carnal circumcision”(Deut. 30:6; Inst.4, 16, 3). Calvin concludes that “we have, therefore, a spiritual promise given to the patriarches in circumcision such as is given us in baptism, since it represented for them[the Jews] forgiveness of sins and mortification of the flesh”(Inst.4, 16, 3). Calvin argues that the symbols of the promise represent the same thing, “namely, **regeneration”(**Inst.4, 16, 4). For Calvin it appears “incontrovertible” that baptism has taken the place of circumcision “to fulfill the same office among us”(Inst.4, 16, 4).”
https://www.reformedtheology.ca/baptism.html