Circumcision was the way a Jew entered the Covenant with God.
Baptism is the way WE enter the NEW Covenant with God.
Newborn BABIES were Circumcised at 8 days old. These babies were raised in the Jewish faith by their parents/guardians.
Newborn BABIES are now Baptized. These babies are raised in the Christian faith by their parents/guardians.
EVERY OT Type has an NT fulfillment.
EVERY NT Fulfillment is more glorious and perfect than its OT Type – WITHOUT exception.
Paul uses the terms, “circumcision of the heart” and the “circumcision of Christ” (Rom. 2:29, Col. 2:12-17) to describe the reality of Circumcision being a spiritually inward act, not merely an outward sign. The Old Testament type that was Circumcision is now Baptism. And, whereas, Circumcision was only applied to male Jews – Baptism applies to ALL in the Christian family.
Finally – the Early Church Fathers were UNANIMOUS in the teaching that this was an APOSTOLIC TEACHING:
Irenaeus
"He [Jesus] came to save all through himself; all, I say, who through him are reborn in God: INFANTS AND CHILDREN, and youths, and old men. Therefore he passed through every age, becoming an infant for infants, sanctifying infants; a child for children, sanctifying those who are of that age . . . [so that] he might be the perfect teacher in all things, perfect not only in respect to the setting forth of truth, perfect also in respect to relative age" (Against Heresies 2:22:4 [A.D. 189]).
Hippolytus
"BAPTIZE FIRST THE CHILDREN, and if they can speak for themselves let them do so. Otherwise, let their parents or other relatives speak for them" (The Apostolic Tradition 21:16 [A.D. 215]).
Origen
"Every soul that is born into flesh is soiled by the filth of wickedness and sin. . . . In the Church, baptism is given for the remission of sins, and, according to the usage of the Church, baptism is given EVEN TO INFANTS. If there were nothing in infants which required the remission of sins and nothing in them pertinent to forgiveness, the grace of baptism would seem superfluous" (Homilies on Leviticus 8:3 [A.D. 248]).
"The Church received FROM THE APOSTLES the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of the divine sacraments, knew there are in everyone innate strains of [original] sin, which must be washed away through water and the Spirit" (Commentaries on Romans 5:9 [A.D. 248]).
Cyprian of Carthage
"As to what pertains to the case of infants: You [Fidus] said that they ought not to be baptized within the second or third day after their birth, that the old law of circumcision must be taken into consideration, and that you did not think that one should be baptized and sanctified WITHIN THE EIGHTH DAY AFTER HIS BIRTH. In our council it seemed to us far otherwise. No one agreed to the course which you thought should be taken. Rather, we all judge that the mercy and grace of God ought to be denied to no man born" (Letters 64:2 [A.D. 253]).
Gregory of Nazianz
"Do you have an INFANT CHILD? Allow sin no opportunity; rather, LET THE INFANT BE SANCTIFIED FROM CHILDHOOD. From his most tender age let him be consecrated by the Spirit. Do you fear the seal [of baptism] because of the weakness of nature? Oh, what a pusillanimous mother and of how little faith!" (Oration on Holy Baptism 40:7 [A.D. 388]).
John Chrysostom
"You see how many are the benefits of baptism, and some think its heavenly grace consists only in the remission of sins, but we have enumerated ten honors [it bestows]! For this reason WE BAPTIZE EVEN INFANTS, though they are not defiled by [personal] sins, so that there may be given to them holiness, righteousness, adoption, inheritance, brotherhood with Christ, and that they may be his [Christ’s] members" (Baptismal Catecheses in Augustine, Against Julian 1:6:21 [A.D. 388]).
Augustine
"What the universal Church holds, not as instituted [invented] by councils but as something always held, is most correctly believed to have been handed down by apostolic authority. SINCE OTHERS RESPOND FOR CHILDREN, SO THAT THE CELEBRATION OF THE SACRAMENT MAY BE COMPLETE FOR THEM, it is certainly availing to them for their consecration, because they themselves are not able to respond" (On Baptism, Against the Donatists 4:24:31 [A.D. 400]).
"The custom of Mother Church in BAPTIZING INFANTS IS CERTAINLY NOT TO BE SCORNED, nor is it to be regarded in any way as superfluous, nor is it to be believed that its tradition is anything except apostolic" (The Literal Interpretation of Genesis 10:23:39 [A.D. 408]).