Infants and children are born with sin (Ps 51:5). Therefore they also need to be born again.
The promise of baptism for the remission of sins is also given to the children (Acts 2:38-39). Children were never excluded from God's covenant with His people (Gen 17:9-14). We must not forbid children from receiving salvation since the Lord Jesus Himself loves little children, and does not reject them (see Lk 18:15-17). In the early church, entire households were baptized (Acts 16:15, 32-34; 18:8; 1Cor 1:16). Children and infants are, of course, part of the household.
Children were healed of their diseases through their parents' faith (Mt 15:28). By the same token, children and infants may be baptized based on the faith of their parents (Jn 4:49-51). However, we must also keep in mind that it is the grace of God and the cross of Christ, not the conscious choice of humans, that gives baptism its effect. So even if children cannot make a conscious choice to receive God's grace, they should not be excluded from God's grace.
Old Testament types for baptism also teach infant baptism. Circumcision prefigures baptism (Col 2:11-12). In the Old Testament the male infants of the chosen people are circumcised on the eighth day (Lev 12:2-3), prefiguring infant baptism. Crossing of the Red Sea also prefigures the New Testament baptism (1Cor 10:1-2). The Israelites, including the children and infants, crossed the Red Sea (Ex 10:9-10, 24; 12:31). The children and infants were not left in the land of bondage. In the same way, children and infants must also be baptized to be cleansed of their sins and be released from the bondage of Satan.