What would happen to a baby's immune system if they were born without a thymus?

If this were to happen the infant would most likely be
prone to more frequent and serious infections because the thymus gland plays a role in
the defense mechanisms of the body. Other immunologic organs like the spleen and groups
of tonsils would attempt to protect the host.

Newborn
infants have an immature immunologic system that develops over months and years. All
newborns are more susceptible to infection for this reason. Some immunities are gained
from the mother at birth, others are received from the mothers milk (breastfeeding), and
still others are received from coming into contact with an offending pathogen. Childhood
immunizations also tremendously help to fight off invading pathogenic
microorganisms.