In "Save the Clam", Great Great Grandfather Griffin, and presumably the ancestors of Glenn Quagmire and Joe Swanson, went to The Drunken Clam for the first time. After being served by Horace's great great grandfather, and getting a little tipsy, they had a conversation about their inevitable deaths, and shortly after decided that The Drunken Clam would be the beer drinking hangout, that they'd go to after work every day until then, thus beginning The Griffin Family tradition of going to The Drunken Clam.
Great Great Grandfather Griffin's death he mentioned, was getting so old and senile, that he would end up in a wheelchair. With age, he would also go completely insane and have to be put into an asylum. His death happened one day, while he was given his monthly dose of outdoor freedom. As he sat in his wheelchair outside, he stared at the ocean ahead and exited peacefully.
Sometime between these two moments in his life, he must have married a woman, most likely named Great Great Grandmother Lois, of whom he had children with, otherwise The Griffin Family line would not have been continued and Peter would have never been born, which he was, therefore I deduce that he must have gotten married and had sex without a condom, impregnating his wife, who decided to keep the baby or babies and after these babies were born, they survived through infancy, and childhood, and adolescence, and adulthood, and ...