Enoch Jr. was born in Atlantic City on December 16, 1912, shortly after the Commodore Louis Kaestner was imprisoned for election fraud and Nucky Thompson had succeeded him as the new Treasurer of Atlantic County, New Jersey.
According to his father, Enoch Jr. was a little and frail child, likely premature, and he was terrified of holding or even looking at him. Being busy with his new appointment, Nucky opted to leave the baby alone for days with the sole company of his mother. It wasn't until several days later when Nucky returned home and finally decided to hold him. To his horror, he discovered that Enoch Jr. had been dead for days and that Mabel, in complete denial, had continued to dress him, wash him and act as if he was alive in general. For this reason the exact date and circunstances of Enoch Jr.'s death remain unclear and the date of December 22nd carved on his grave likely stands for the day that Nucky discovered his body. After Enoch Jr.'s funeral Mabel fell in depression and ultimately committed suicide in January 19, 1913. ("A Return to Normalcy")
Nucky rarely brings the subject that he ever had a son, even when talking about the death of his wife, which he tends to blame on tuberculosis instead - the actual fate of his younger sister, Susan Thompson ("Boardwalk Empire", "Georgia Peaches").