We know that a man named Shakespeare wrote the plays. He put his name on them.
Contemporary documents show that this man was named William Shakespeare. He was the son of a glover and educated at Stratford Grammar School in the town of Stratford-Upon-Avon. We know he married Anne Hathaway. We know he was an actor and we know he died in 1616. This is what the documents say and there is no convincing evidence to the contrary to suggest he did not write the plays.
All that tells us is that there was a man from Stratford called Shakespeare and that, for whatever reason, his name appeared on a number of plays attributed to him. That does not prove that he wrote them.  We don’t even know if that is how he spelt his name. The only surviving example of Shakespeare’s writing are six scratchy signatures spelt several different ways. There is also significant evidence to suggest he did not write the plays. What we know of his education suggests he would not have had the necessary schooling to produce works of the calibre attributed to his name.
[P1] Shakespeare's name is on the plays in black and white. [P2] There is no compelling evidence to the contrary to suggest he did not write the plays. [P3] Therefore, the logical conclusion is that Shakespeare wrote the plays.
[Rejecting P3] There is significant evidence to suggest that Shakespeare did not possess the necessary education to write the plays and sonnets.