Regarding the consequences of the original sin:

Catholics believe that what Adam primarily lost by his sin, for
himself and the human race, was sanctifying grace.  This is basically
a share in the Divine life.  Take a rock and make it able to talk:
what God does to a human being through sanctifying grace is similar.
It makes such a one able to live on a plane that is above the powers
of any possible creature.  This is the "everlasting life" that the New
Testament speaks of.

What Christ did when he came was to restore this life of sanctifying
grace to the human race.  He instituted the Sacraments as the means by
which this life is given to people, and its increase fostered.

The absence of sanctifying grace at death means automatic exclusion
from Heaven.  The nature of Heaven is such that it's impossible for a
human being to have any part in it without the gift of sanctifying
grace.  To use my example, it would be like taking that rock and
attempting to hold a conversation with it: rocks cannot talk.  Neither
can human beings live in Heaven without sanctifying grace.

This all obviously applies equally well to infants or adults, since
both have souls.  Infants must be baptized, therefore, or they cannot
enter into Heaven.  They too need this form of life in them, or they
cannot enter into Heaven.

Turning it around, infant baptism is good supporting evidence for the
Catholic belief in sanctifying grace.  Unless Baptism causes some
change in an infant's soul, there is no particular reason to insist on
the practice.  Yet infant Baptism was probably practiced by the
Apostles themselves, and was *certainly* part of the Church shortly
thereafter.