All Koreans advance their age on January 1st. They count the nine months gestation as their first year, so even if a Korean were born on March 15, for example, the following January 1st, they would be considered two years old, and increase their age by one every January 1st.
If an American asks a Korean how old they are, they will typically ask in return, "Korean age or American age?"
I was thinking young Kim simply asked why there were so many people celebrating Jan 1st, and his parents just told him all the New Year’s parades were people celebrating his birthday.