One question that comes up with regard to the Didache is, when was it written? Is it a first or second century document? While there is no unanimous consensus on this question, a number of scholars believe that the Didache was actually produced in the second century. If so, this would comport with the observations of Origen and Tertullian regarding infant baptism taking place in their day.
Stanley Burgess observes that the Didache is "an early second century document" (The Holy Spirit: Ancient Christian Traditions, page 21).
Howard Vos simply writes that the Didache "is also believed to have originated in Alexandria (though some think it came from Syria), probably during the first decades of the second century" (Exploring Church History, Page 12).
Moreover, The Westminster Handbook to Patristic Theology states that the Didache "comes from the late first to mid-second century, and is more in the style of a compilation of practices for a group of churches than the work of a single theologian-author" (page 100).
But the magisterial study by W. H. C. Frend dates the Didache circa A.D. 70 (See The Rise of Christianity, page 29). So we have respected scholars from both sides offering (as usual) possible, but contrary opinions on this
important matter. Personally, I think the evidence favors the second century
dating. I am certain that some would heavily dispute this conclusion or
question my motivation in deciding on that date. But as I said earlier, the
contents in the work makes me incline toward the second century dating for the Didache. This factor along with what other writers say about the practice of infant baptism in antiquity influences my decision.
I think that baptism started out as the immersion of believing adults (Mt 28:18-20; Acts 8:12-13). However, in time, infants began to be baptized on what Jaroslav Pelikan calls "biblical warrants that [are] somewhat ambiguous." This famed and late ecclesiastical historian argues that "the first incontestable evidence for the practice [of infant baptism] appeared around the end of [the second] century" (Cf. The Christian Tradition 1:290-292 and 1:316-318). As is well known, Tertullian vehemently rejected the practice of infant baptism (Baptism 18.5).
So I would say that the historical evidence indicates that there were different kinds of baptism from the second century onward, though it seems that the Primitive Christians started out immersing new believers under water when they baptized them (Acts 8:34-39).
Harold O.J. Brown writes that "Although a critical reaction against its [the Didache's] significance took place in the earlier part of this century, its place as a valuable composition of the earliest of Apostolic Fathers texts is secure."
I would add that the Didache does help us to understand what was happening
in second century Christianity. This does not mean, however, that all
Christians practiced infant baptism in the second century. It also seems
highly unlikely that all believers in Christ practiced sprinkling at that time (Compare Hermas, ANF Series, 2.49; Apostolic Constitutions 7.53, Tertullian ANF Series, 3.669-671).