With original guilt being established by Scripture, that in Adam all die, even those who had not sinned after the similitude of Adam's sin, we must go on to ask, then how is an infant saved?
In the exact same manner as an adult and under no other Gospel but the Gospel of Christ. Infants enter heaven the same way we do, through Jesus Christ. None here will likely believe an infant can be saved through baptism, and we (reformed Baptists) affirm no such thing.
What I believe is that the infant is saved because it is elect. This is the selfsame reason anyone, infant or adult, is saved. As it is written,
"Blessed be the God and Father of our Lord Jesus Christ, who hath blessed us with all spiritual blessings in heavenly places in Christ: According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love: Having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will, To the praise of the glory of his grace, wherein he hath made us accepted in the beloved."
Sometimes Romans 8:29-30 is referred to as the golden chain of redemption, "For whom he did foreknow, he also did predestinate to be conformed to the image of his Son, that he might be the firstborn among many brethren. Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified."
Certainly it is not a stetch of Scripture truth to include infants in the foreknowledge (fore-love) and foreordination of God. Our Lord Jesus, slain from the foundation of the world, purchased with His own blood elect sons and daughters of both infants and adults.
And we would not dare to say that the infant is saved apart from regeneration. Christ our Lord has said, "Ye must be born again." And so must they. The infant is elect for no reason other than what the Scripture declares, "according to the good pleasure of His will." And is called in death, justified, and glorified by the operation of God no different than we are. On this point Spurgeon said,
No doubt, in some mysterious manner the Spirit of God regenerates the infant soul, and it enters into glory made meet to be a partaker of the inheritance of the saints in light. That this is possible is proved from Scripture instances. John the Baptist was filled with the Holy Ghost from his mother's would. We read of Jeremiah also, that the same had occurred to him; and of Samuel we find that while yet a babe the Lord called him. We believe, therefore, that even before the intellect can work, God, who worketh not by the will of man, nor by blood, but by the mysterious agency of his Holy Spirit, creates the infant soul a new creature in Christ Jesus, and then it enters into the "rest which remaineth for the people of God." By election, by redemption, by regeneration, the child enters into glory, by the selfsame door by which every believer in Christ Jesus hopes to enter, and in no other way.
Amen and Amen.