The Epistle of Barnabas is an early Christian writing from the middle of the second century. It is also a very early Christian witness to how pervasive the doctrine that baptism is salvific truly is:
Further, what says He? "And there was a river flowing on the right, and from it arose beautiful trees; and whoever shall eat of them shall live for ever." This meaneth, that we indeed descend into the water full of sins and defilement, but come up, bearing fruit in our heart, having the fear of God, and trust in Jesus in our spirit. (Epistle of Barnabas 11:10)
In this text, the person who is baptised is said to have their sins removed out of the water, showing that water baptism is the instrumental means of regeneration, only strenghtened by the fact that a person's nature, as a result of this baptism, is changed, again, showing that regeneration is the result of baptism. Furthermore, the Greek texts speaks of one "ascending" out of the water (αναβαινω), showing that the earliest Christian mode of baptism was that of immersion, consistent with LDS belief and practice.
For further discussion of the biblical and early Chrisitan understanding of baptism, see
Everett Ferguson, Baptism in the Early Church: History, Theology, and Liturgies in the First Five Centuries (Grand Rapids, Mich.: Eerdmans, 2009)