Everything we know about Hamnet Shakespeare is that he was baptised 2 February 1585, Stratford-upon-Avon, one of a pair of twins; and buried, 11 August 1596. He was eleven years old. He was born; he lived; he died. And one more thing: he happened to be the only son of the most famous writer in history.
There is also a body of circumstantial evidence that surrounds the life of Hamnet, is contingent upon it, and may or may not allow us to infer something about him. We know a lot, of course, about his family, especially his father. His twin Judith lived to the age of seventy-seven, and we know a fair bit about her. The names of both twins replicate the names of a Stratford couple, friends and neighbours of the Shakespeares, Hamnet and Judith Sadler, who were Catholic recusants; surely more than a coincidence. Hamnet Sadler is remembered in Shakespeare's will, where his name is spelt, interestingly, ‘Hamlett’.
Certain documented events surround the date of Hamnet's death. When Hamnet died, the Lord Chamberlain's Men were touring in Kent: on 11 August they played the market hall in Faversham. Shakespeare may have been with them.
A few months after the boy's death, Shakespeare re-submitted to the College of Heralds an application for a grant of arms to the Shakespeare family; and in the following year, 1597, he bought a large house, New Place in Stratford.
Most of the Hamnet Shakespeare story is a fabric woven around the pegs of these direct and circumstantial historical data. Some biographers have also brought to bear information from a broader spectrum of facts. Evidence of mortality rates from the Stratford burial records, to account for Hamnet's demise. Evidence about schooling, to flesh out for him an appropriate education. Evidence about housing, family life, employment, the economy, to sketch out for him an illuminating social milieu. All these data can be corroborated, authenticated, endorsed as genuine historical context and assumed as Hamnet Shakespeare's background. But none of it can be connected with him in any definitive way, since the only traces the boy left are those cold, impersonal words telling us that he was born, and that he died.