One question that arises 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--I note that a number of scholars
believe that the Didache was actually produced in the second century. If this belief is accurate, this fact would comport with either Origen or Tertullian's comments regarding the subject of infant baptism.
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,
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 possible, but contrary opinions on this important matter. Personally, I think that 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 the contents in the work make me incline toward the second century dating for the Didache. This along with what other writers say about the practice of infant baptism in antiquity influences my perspective.)
I believe that Christian baptism first involved 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." He argues that "the first incontestable evidence for the practice [of infant baptism] appeared around the end of [the second] century" (See 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 different kinds of baptism occurred from the second century onward, though it seems that Primitive Christians started out immersing new believers under water when they baptized them (Acts
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. Therefore, it seems
highly unlikely that all Christians practiced sprinkling then (Compare Hermas, ANF Series, 2.49; Apostolic Constitutions 7.53). The Bible itself appears to clearly teach baptism by water immersion.