How do the antibodies in colostrum survive the infant’s digestive system?
There are two main differences between adults and newborn babies which allow the passage of antibodies (while maintaining the activity) through the stomach and the resorption in the gut.


The digestive activity of the stomach in newborns is still immature and needs to develop. This results in almost no production of hydrochloric acid (which is responsible for the very low pH in the stomach). It can take up to two years to until the pH in the stomach of children reaches the level of adults (see chapter 5 in reference 1).  Because of this higher pH much more proteins (and other components of the milk like anti-microbial proteins, carbohydrates and lipids) can pass the stomach unaltered.
The other really important feature of newborns is their much greater permeability of their intestine. This allows an efficient transport from the antibodies into the blood stream and where they provide protection. See references 2 and 3 for more details.


References:


Breastfeeding and Human Lactation
Antibodies in  Milk
Intestinal permeability in the newborn