Is it possible to be born with brittle bones?

Yes: It is called Osteogenesis imperfecta and is a genetic disorder. The severity depends on which genes are involved and how many and if they are inherited from one or both parents. No horseplay with these children, no firm handshakes or robust back pats or bear hugs. Their bones are easily fractured and they are not spared the pain of broken bones. Those I have met were humorous intelligent people.