How might a newborn obtain normal flora that soon populates its body?

First, all persons have normal flora, including in / on mucous membranes such as the mouth and vagina. All skin surfaces have normal flora.

A newborn is exposed to its mother's (normal or abnormal) vaginal flora as the neonate passes through the birth canal, past the labia and pubic hair.

In addition, a newborn picks up other people's normal flora everytime the baby is touched. Everyone from nurses, doctors, moms, dads, grandparents, and even siblings contribute bits of their own flora.

Unless someone had a skin or other active infection, usually this mix of floras helps babies to develop stronger immune systems, almost from day one of their lives.