What is the earliest explicit mention of infant baptism?

There are various passages in the New Testament and early Christian writers which have been interpreted to imply or support infant baptism. However, since you ask for explicit mentions, I'm going focus on ones that are unambiguous. Irenaeaus of Lyon's Against Heresies 2:22:4 hangs on the meaning of "born again" in his era.

The first unambiguous discussion of infant baptism is the argument against the practice in Tertullian of Carthage's On Baptism 18 (198-203 CE). I offer two translations:

Tertullian, as translated by Sydney Thelwall (1885)

according to the circumstances and disposition, and even age, of each individual, the delay of baptism is preferable; principally, however, in the case of little children. ... The Lord does indeed say, “Forbid them not to come unto me.” Let them “come,” then, while they are growing up; let them “come” while they are learning, while they are learning whither to come; let them become Christians when they have become able to know Christ. Why does the innocent period of life hasten to the “remission of sins?” More caution will be exercised in worldly matters: so that one who is not trusted with earthly substance is trusted with divine! Let them know how to “ask” for salvation, that you may seem (at least) to have given “to him that asketh.” ... If any understand the weighty import of baptism, they will fear its reception more than its delay

Tertullian, as translated by Alexander Souter (1919):

in view of the circumstances and will, even the age of each person, a postponement of Baptism is most advantageous, particularly, however, in the case of children. ... The Lord indeed says: "Forbid them not to come unto Me." Let them come, then, while they are growing up; let them come while they are learning, while they are being taught whither to come; let them become Christians, when they have been able to know Christ. Why hurries the age of innocence to the remission of sins? Shall we act more cautiously in worldly matters? Shall one to whom earthly substance is not entrusted, be entrusted with heavenly? Let them know how to seek salvation, that you may be seen "to give to him that asketh." ... If any should understand the importance of Baptism, they will be more afraid of its consequences than of its postponement; unimpaired faith is sure of salvation.

The view that Tertullian was the first unambiguous reference to infant baptism was affirmed by Lutheran scholar Heinrich August Wilhelm Meyer (Commentary on Acts [16:15], New York: Funk & Wagnalls, 1883, p. 312).

Importantly, however, as I read it, the Tertullian passage indicates that others are at least considering infant baptism at his time. Tertullian seems to be responding to someone else quoting Jesus statement, "Forbid them not to come unto Me", in favor of infant baptism.

The challenge of such a late dating of infant baptism is that not long thereafter, Origen of Alexandria, who was incredibly knowledgeable and widely traveled, takes the practice for granted as normative:

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 [248 CE])

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 [248 CE])

Around the same time about 252 CE, Cyprian wrote a report from a council of sixty-six bishops affirming that baptism should take place shortly after birth against the view of Fidus that they should be baptized on the eighth day after birth. These sixty-six bishops seem to take infant baptism for granted, and evidently there were no vocal opponents of infant baptism in the conversation. _{(There were several councils of Carthage from 251-254 or so, and it's not clear which one this letter is from.)}

It is clear that we are lacking in reliable records on this topic for early centuries. As Adolf Harnack said, "Complete obscurity prevails as to the Church's adoption of the practice of child baptism" Adolf Harnack, History of Dogma, Volume 2, 1896 [1885], p. 142.

I should also mention that The Apostolic Tradition, an important work with 3rd century or earlier content, includes this passage:

“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” (21:16)

However, The Apostolic Tradition has an unclear transmission and editorial history, and the majority of the work seems to assume adult converts, so it isn't very helpful in dating the emergence of the practice.

In short, our first clear source on infant baptism is an opponent around 200 CE, but our next sources around 250 CE show support for infant baptism was widespread, and regard the practice as old and uncontroversial.