The earliest (Christian), witness to Christian baptism is found in the earliest systematic witness to the 1st century Christian community, the document known as 'Didache'. This document is dated to within the 1st century AD.
In that document they insist on the full immersion of an informed adult believer, and make a clear distinction between immersion and sprinkling:
Chapter 7:
1 But concerning baptism, thus baptize ye: having first recited all these precepts, [that's chapters 1-6, which is a long list of doctrines and practices, which a child cannot understand] in the name of the Father, and of the Son, and of the Holy Spirit in running water.
2 but if thou hast not running water, baptize [immerse] in some other water, and if thou canst not baptize in cold, in warm water;
3 but if thou hast neither, pour [different word to baptize] water three times on the head, in the name of the Father, and of the Son, and of the Holy Spirit.
4 But before the baptism, let him who baptizeth and him who is baptized fast previously, [not what you expect of a child] and any others who may be able. And thou shalt command him who is baptized to fast one or two days before.
Furthermore, only those who were baptized could take communion:
Chapter 9:
5 And let none eat or drink of your Eucharist but such as have been baptized into the name of the Lord, for of a truth the Lord hath said concerning this, Give not that which is holy unto dogs.
So you had a closed fellowship, based on being informed of and baptized into a formal set of beliefs, which were inaccessible to a child.
Infant baptism was a much later development. Certain quotes from the Early Fathers are offered as 'evidence' that infants were baptized at an early stage in church history, but many of them are out of context, or simply do not say what is claimed. The earliest undisputed reference to infant baptism is not found until the late 2nd, early 3rd century.
Christian witnesses to baptismal praxis follow.
'From writers of unquestionable authority, it is evident, that the primitive christians continued to baptize in rivers, pools, and baths, until about the middle of the 3rd century.
Justin Martyr says, that they went with the catechumens to a place where there was water, and Tertullian adds, that the candidates for baptism made a profession of faith twice, once in the church, and then again when they came to the water, and it was quite indifferent whether it were the sea, or a pool, a lake, or a river, or a bath. Such are the accounts given by Justin Martyr in his Apology, and by Tertullian on baptism as quoted by Robinson.
The sacrament of baptism, says Mosheim, was administered in the first century, without the public assemblies, in places appointed and prepared for that purpose, and was performed by immersion of the whole body in the baptismal fount.
Ecclesiastical History, Philadelphia edition, vol. 1. p. 126.
Tertullian, another 2nd century witness:
Upon that, we are immersed (Latin: mergo, to dip, to immerse) three times, making a somewhat ampler pledge than the Lord has appointed in the gospel.
Then, when we are taken up, we tast first of all a mixture of milk and honey. Then, from that day, we refrain from the daily bath for a whole week.
Tertullian, c. 211, 3.94.
"Baptism itself is a corporal act by which we are plunged into the water, while its effect is spiritual, in that we are freed from our sins"
Baptism 7:2
Irenaeus, 190:
"`And (Naaman) dipped himself . . . seven times in the Jordan' (2 Kgs. 5:14). It was not for nothing that Naaman of old, when suffering from leprosy, was purified upon his being baptized, but (this served) as an indication to us. For as we are lepers in sin, we are made clean, by means of the sacred water and the invocation of the Lord, from our old transgressions, being spiritually regenerated as new-born babes, even as the Lord has declared: `Except a man be born again through water and the Spirit, he shall not enter into the kingdom of heaven'"
(Fragment 34).
Justin Martyr made it clear that baptism required knowledge, an informed decision an infant could not make:
And this washing is called illumination, because they who learn these things are illuminated in their understandings. And in the name of Jesus Christ, who was crucified under Pontius Pilate, and in the name of the Holy Ghost, who through the prophets foretold all things about Jesus, he who is illuminated is washed.
(Justin Martyr, First Apology of Justin Martyr, Chapter 61, Christian Baptism, Vol. 1,)
Then these fourth century witnesses:
Cyril of Jerusalem, 360:
For as he who plunges into the waters and is baptized is surrounded on all sides by the waters...
Basil of Casearea, 370:
How then do we become in the likeness of his death? We were buried with him through baptism....How then do we accomplish the descent into Hades?
We imitate the burial of Christ through baptism. For the bodies of those being baptized are as it were buried in water.
Ambrose, 375:
So therefore also in baptism, since it is a likeness of death, without doubt when you dip and rise up there is made a likeness of the resurrection.
375 AD Basil the Great: "This then is what it means to be `born again of water and Spirit': Just as our dying is effected in the water [Rom. 6:3, Col. 2:12-13], our living is wrought through the Spirit. In three immersions and an equal number of invocations the great mystery of baptism is completed in such a way that the type of death may be shown figuratively, and that by the handing on of divine knowledge the souls of the baptized may be illuminated. If, therefore, there is any grace in the water, it is not from the nature of water, but from the Spirit's presence there" (The Holy Spirit, 15:35).
381 AD Ambrose of Milan: "Although we are baptized with water and the Spirit, the latter is much superior to the former, and is not therefore to be separated from the Father and-the Son. There are, however, many who, because we are baptized with water and the Spirit, think that there is no difference in the offices of water and the Spirit, and therefore think that they do not differ in nature. Nor do they observe that we are buried in the element of water that we may rise again renewed by the Spirit.
The Holy Spirit 1:6[75-76].
John Chrysostom, 390:
Exactly as in some tomb, when we sink our heads in water, the old man is buried, and as he is submerged below, he is absolutely and entirely hidden...