St Paul clearly speaks on sin/death throughout Romans, where Adam is shown as transmitting death with sin. Read 5:12
The Didache
After the foregoing instructions, baptize in the name of the Father, and of the Son, and of the Holy Spirit, in living [running] water. If you have no living water, then baptize in other water, and if you are not able in cold, then in warm. If you have neither, pour water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit. Before baptism, let the one baptizing and the one to be baptized fast, as also any others who are able. Command the one who is to be baptized to fast beforehand for one or two days (Didache 7:1 [ca. A.D. 70]).
Justin Martyr
As many as are persuaded and believe that what we [Christians] teach and say is true, and undertake to be able to live accordingly, and instructed to pray and to entreat God with fasting, for the remission of their sins that are past, we pray and fast with them. Then they are brought by us where there is water and are regenerated in the same manner in which we were ourselves regenerated. For, in the name of God, the Father… and of our Savior Jesus Christ, and of the Holy Spirit [Matt. 28:19], they then receive the washing with water. For Christ also said, “Unless you are born again, you shall not enter into the kingdom of heaven” (First Apology 61 [A.D. 151]).
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
Where there is no scarcity of water the stream shall flow through the baptismal font or pour into it from above; but if water is scarce, whether on a constant condition or on occasion, then use whatever water is available. Let them remove their clothing. 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]).
Recognitions of Clement
But you will perhaps say, ‘What does the baptism of water contribute toward the worship of God?’ In the first place, because that which has pleased God is fulfilled. In the second place, because when you are regenerated and born again of water and of God, the frailty of your former birth, which you have through men, is cut off, and so . . . you shall be able to attain salvation; but otherwise it is impossible. For thus has the true prophet [Jesus] testified to us with an oath: “Verily, I say to you, that unless a man is born again of water . . . he shall not enter into the kingdom of heaven” (Recognitions of Clement 6:9 [A.D. 221]).
Origen
The Church received from the apostles the tradition of giving baptism even to infants. The apostles, to whom were committed the secrets of divine sacraments, knew there is 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
[l]t behooves those to be baptized . . . so that they are prepared, in the lawful and true and only baptism of the holy Church, by divine regeneration, for the kingdom of God . . . because it is written “Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God” (Epistles 72 [73]: 21 [A.D. 252]).
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]).
In the saving sacraments, when necessity compels and when God bestows his pardon, divine benefits are bestowed fully upon believers, nor ought anyone be disturbed because the sick are poured upon or sprinkled when they receive the Lord’s grace" (Letter to a Certain Magnus 69(76):12 [A.D. 254]).
Ambrose of Milan
The Church was redeemed at the price of Christ’s blood. Jew or Greek, it makes no difference; but if he has believed, he must circumcise himself from his sins [in baptism (Col. 2:11-12)] so that he can be saved . . . for no one ascends into the kingdom of heaven except through the sacrament of baptism… “Unless a man be born again of water and the Holy Spirit, he cannot enter the kingdom of God” (On Abraham 2:11:79-84 [A.D. 387]).
Paul alludes to infant baptism when he tells us that baptism replaces circumcision (Colossians 2:11). This is why the early Christians baptized infants on the eighth day after birth. The eighth day after birth is when Jewish boys were circumcised. Those who contend that infants shouldn’t be baptized have a faulty understanding of what baptism is. With baptism there is an infusion of grace, grace is what enables a child being raised in the faith to understand his or her need for God. The early church administered baptism in three ways; by immersion, sprinkling and pouring.
Tertullian
[N]o one can attain salvation without baptism, especially in view of the declaration of the Lord, who says, “Unless a man shall be born of water, he shall not have life” (On Baptism 12:1 [A.D. 203]).
The absence of sanctifying grace in a child is a real privation, it is the want of something that should have been in him according to the Divine plan.
