WHY then babies are born into sin after Jesus was killed on the cross to forgive sins?

WHY then babies are born into sin after Jesus was killed on the cross to forgive sins?

The only mention in the gospels is of adults being baptized. “Faith and baptism were always connected with one another; and thus it is in the highest degree probable . . . that the practice of infant baptism was unknown at this period [in the first century]. . . . That it first became recognized as an apostolic tradition in the course of the third century, is evidence rather against than for the admission of its apostolic origin.”—History of the Planting and Training of the Christian Church by the Apostles (New York, 1864), p. 162. Augustus Neander

when this tradition began?