The underlying foundation for the practice of infant baptism is the concept that God establishes His covenants throughout history with family units: with believers and their children. God’s covenants, rather than leaving the children outside and waiting for them to make a voluntary choice to enter the covenant and become one of God’s people, is instead always reaching forward to claim the next generation as belonging to God from the beginning of their lives. This does not imply that the child need not make the choice to exercise repentance and faith. Life in covenant with God is a life of repentance and faith in the work of Jesus Christ, along with faith-filled obedience to God’s word. The generational aspect of God’s covenant means that children of the covenant start out life as belonging to God, and should be trained as such: learning to view God as their Father, love Him, worship Him, and obey Him in accordance with their natural mental development from their earliest days. This is in contrast to viewing children of believers as “separate from Christ, excluded from the commonwealth of Israel, and strangers to the covenants of promise, having no hope and without God in the world” (Ephesians 2:12) until they are old enough to have a cognitive conversion experience.
As a side note, teaching young children to worship God in church, memorize Bible verses, pray to God as Father, and obey God’s word is more consistent with viewing them as “little believers in training” than “little pagans in rebellion against God”. Most faithful Christian parents intuitively do these things, expecting a positive, receptive response from the child. Not because of belief in the child’s inherent goodness, but because of faith that God is working on the child’s heart already through the appointed means of child training and discipline.