Certainly; if there were no way of saving children but by the Gospel, this conclusion [i.e. that infant salvation would be impossible] would be inevitable. The Gospel saves none but by faith. But the Gospel has nothing to do with infants, nor have Gospel ordinances any respect to them. The Gospel has to do with those who hear it. It is good news; but to infants it is not news at all. They know nothing of it. The salvation of the Gospel is as much confined to believers, as the baptism of the Gospel is. None can ever be saved by the Gospel who do not believe it.
Consequently, by the Gospel no infant can be saved. It is expressly, with respect to such as hear it, that the Gospel is here said to be salvation by faith, and condemnation by unbelief. “Go ye into all the world, and preach the Gospel to every creature. He that believeth and is baptized shall be saved; but he that believeth not shall be damned.” Here the salvation and the condemnation respect those to whom the Gospel comes. Infants are saved by the death of Christ, but not by the Gospel not by faith. Adults are saved by faith, not from the virtue of faith, but it is of faith that it might be by grace. Infants who enter heaven must be regenerated, but not by the Gospel. Infants must be sanctified for heaven, but not through the truth as revealed to man. We know nothing of the means by which God receives infants; nor have we any business with it.
–Alexander Carson, Baptism in Its Mode and Subjects. With a Sketch of His Life by John Young. Philadelphia: American Baptist Publication Society, 1845. p. 173; paragraph divided for easier readability)