Can you be born with liver cancer?
I believe that you can be born with a genetic predisposition and/or liver damage that can lead to liver cancer later, rather than being born with liver cancer itself. A hepatitis infection, for example, could lead to cirrhosis and possibly liver cancer.
There's a rare form of liver cancer called hepatoblastoma that happens in infants under the age of 3, but I'm not sure if these babies are actually born with it or develop it that quickly.
Having familial adenamatous polyposis (FAP), Beckwith-Wiedemann syndrome, and very low birthweight all put a baby for higher risk of liver cancer, too.