His date of birth is not known, just when he was baptized. But his date of death is known as the will was probated. There's about as much of documentary evidence as you would imagine from a middle class English man of his time. Maybe a little more. (Ducks behind a rock while the Oxfordians load cannons and fire.)

I hold the outlandish belief that William Shakespeare was William Shakespeare. And even if he were an alien, it would have little to do with his texts. Bacon, Oxford, Mercutio Florio. There's been a ton of conjecture on who he was. Ben Jonson seemed to think WS was WS. Not to be tautological, but it's good enough for me.