Adam and Eve were the first created humans. Naturally they were without sin. They did sin, however, and the tainted the entire human race, including infants. Original sin was documented by Augustine, but it was not invented by Augustine. ALL have sinned and come short of the glory of God,,,,,,,,and in need of redeeming grace.
I grew up in the church and even believed, but I did not grow into a redemptive state. I had to believe that Jesus died for me and experience being born again. If any child is saved, it is by the hand of God in grace. Even in the Calvin quote he has infants saved by grace and others passed by as reprobate..........yes, infants! Amazing!
Even theology has wishful thinking by times.
Calvin also sprinkled (baptized) infants as a covenant promise to raise them in the Christian religion, a continuation of circumcision and its covenant promise. It did not save them in the NT sense, but committed them to God.
Cheers,
Jim