1. Unless you believe baptism imparts grace, infant baptism will always remain a mystery to you. I believe it does impart grace, based on John 3:5, Acts 2:38, Acts 22:16, Romans 6:4 and many other passages. Of course 100% of the early church fathers taught baptismal regeneration. I realize some here think these men were apostate but they were not. They constantly railed against apostasy. Significantly, they reduced to writing many of the practices and beliefs extant in the early Christian community that were so widely held they aren't even mentioned in scripture.John 3:5 reads: "Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God."
Infant baptism and the resulting theology troubles me. The notion of baptizing someone who has absolutely no choice in the matter is just wrong. Imagine grabbing a 30-year-old nonbeliever off the street and baptizing them because you think it will impart some sort of grace toward them and bring them to salvation.
In the epistle to those at Phillipi, we read that people should work out their own salvation with fear and trembling. Nothing in there requiring them to get baptized at the same time, nor teaching them to baptize their children.
2. There were in fact young children who were baptized in N.T. times. The N.T. gives four (4) instances where entire households were baptized. In those days a household included extended family and servants. A household may be as large as 25-30 people. For none of these four households to have young children would be against the greatest of odds. Remember also that Peter said immediately after his command to repent and be baptized,"For the promise is for you and your children . . . ." " And they were bringing even their babies to Him so that He would touch them, but when the disciples saw it, they began rebuking them. 16 But Jesus called for them, saying, “Permit the children to come to Me, and do not hinder them, for the kingdom of God belongs to such as these." This is pretty strong evidence that Jesus approved of infant baptism.