That is not really accurate as we can trace infant baptism being debated to Tertulian around the late 100s. When St. Augustine was in the late 300's the matter was decided in favor of infant baptism. The NT and Didache are not clear on the practice, hence the difference in opinions and reasons to baptize as infants or wait. The NT only mentions "households" or individuals being baptized, which historically we assume would have included babies. This along with the practice of families with babies converting to Judaism and everyone needing to be immersed in the Mikvah leads many to believe in infant baptism. Basically it was debated very quickly after the Apostles were gone as we have no explicit directive handed down. All that said, I believe there is no clear answer from scripture or Tradition, so if one wants to wait that is fine and there are solid reasons.
Happy to discuss this further, but probably in another thread
That does sound nice, I like bringing the baby into the community of Christians and to God.
In the Lutheran Church (as well as others) the liturgy with Baptism is similar. The baby is baptized and then introduced to the community, who promises to assist in raising the child in the faith. Then around 12-15 years old the child makes "Confirmation" where he or she confirms their belief in the faith, God, etc. in front of the community; this would be similar to the Bar Mitzvah in Judaism, so again there are ancient traditions tied to the practice. At this point they are a full member of the community and church. Baptism is a means of grace and remission of sins provided by Christ's sacrifice.