Crispus, the ruler of the synagogue, believed in the Lord, together with all his household; and many of the Corinthians hearing Paul believed and were baptized. (Acts 18:8)
One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to give heed to what was said by Paul. And when she was baptized, with her household… (Acts 16:14)
The Orthodox Church, like most of the ancient traditions of Christianity have interpreted passages like those above to mean that everyone in a household was baptized, and that would include the children of all ages. Those traditions which have a strong sacramental and incarnational dimension, understand that God works salvation in and through the things of this world because God is interested in the entire human God created – not just their souls, but bodies as well. This thinking finds support in some other scriptural passages.
For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband. Otherwise, your children would be unclean, but as it is they are holy. (1 Corinthians 7:14)
The children, even of a mixed marriage between a believer and non-believer, are claimed to be holy, purely by being the child of a believing parent. We baptize such children in recognition of their holiness – not to make them holy. We are simply recognizing what God is bringing about in the world.
At that time the disciples came to Jesus, saying, “Who is the greatest in the kingdom of heaven?”  And calling to him a child, he put him in the midst of them,  and said, “Truly, I say to you, unless you turn and become like children, you will never enter the kingdom of heaven.  Whoever humbles himself like this child, he is the greatest in the kingdom of heaven.  “Whoever receives one such child in my name receives me;  but whoever causes one of these little ones who believe in me to sin, it would be better for him to have a great millstone fastened round his neck and to be drowned in the depth of the sea. (Matthew 18:1-6)
Whoever receives one such child in Christ’s name, receives Christ! So in the Church we do receive such children and thereby receive Christ in our midst. The child brings Christ to us. The child is for us an example of greatness – the greatest in the kingdom of heaven according to Christ. The child shows us the way to enter the Kingdom. Thus when we baptize the child it is not only that we bring the child to Christ, but the child brings Christ to us. We not only lead the child to the kingdom, but that child leads us to the kingdom. The baptism of children is also for our salvation!
And they were bringing children to him, that he might touch them; and the disciples rebuked them.  But when Jesus saw it he was indignant, and said to them, “Let the children come to me, do not hinder them; for to such belongs the kingdom of God.  Truly, I say to you, whoever does not receive the kingdom of God like a child shall not enter it.” (Mark 10:13)
The Kingdom of God belongs to the children who are brought to the Church to be touched by Christ. The child teaches us how to receive the Kingdom of God. We have much to learn at and from every infant baptism.