Yes, documents from 400 years ago could be lost, yet we have letters from Thomas Nashe, Philip Massinger, Gabriel Harvey, Samuel Daniel, George Peele, Edmund Spenser, Michael Drayton, George Chapman, Ben Jonson, and William Drummond, Anthony Mundy, John Lyly, Thomas Kyd, Robert Greene, Christopher Marlowe and others, many of them lesser writers.
FORBES: Yes, Shakespeare Really Did Write Shakespeare