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Ben Jonson contributed a poem to the dedications printed in the First Folio:
To the memory of my beloved, Mr. William Shakespeare and what he hath left us... While I confesse thy writings to be such, As neither Man, nor Muse, can praise too much... Soule of the Age ! The applause ! delight ! the wonder of our Stage ! ...Thou art a Moniment, without a tombe, And art alive still, while thy Booke doth live, And we have wits to read, and praise to give... I should commit thee surely with thy peeres, And tell, how farre thou dist our Lily out-shine, Or sporting Kid or Marlowes mighty line. And though thou hadst small Latine, and lesse Greeke, From thence to honour thee, I would not seeke For names; but call forth thund'ring schilus, Euripides, and Sophocles to vs, Paccuvius, Accius, him of Cordova dead, To life againe, to heare thy Buskin tread... He was not of an age, but for all time ! ...For a good Poet's made, as well as borne. And such wert thou. Looke how the fathers face Lives in his issue, even so, the race Of Shakespeares minde, and manners brightly shines In his well toned, and true-filed lines, In each of which, he seemes to shake a Lance, As brandish't at the eyes of Ignorance. Sweet swan of Avon! ...Shine forth, thou Starre of Poets, and with rage, Or influence, chide, or cheere the drooping Stage; Which, since thy flight fro' hence, hath mourn'd like night, And despaires day, but for thy Volumes light.
Shakespeare wrote Shakespeare's plays, there's simply no basis to claim otherwise. An older, and dying poet / playwrite made note of the fact that what is now called Henry VI, pt 3 had already become a hit, and in fact was apparently what made Shakespeare a star -- the actual box office receipts were recorded and the record has survived, and apparently that one play outsold all other contemporary plays combined. WS was actor and playwrite by 1592.
...there is an vpstart Crow, beautified with our feathers, that with his Tygers hart wrapt in a Players hyde, supposes he is as well able to bombast out a blanke verse as the best of you: and beeing an absolute Iohannes fac totum [Johnny do-it-all], is in his owne conceit the onely Shake-scene in a countrey... -- Greenes Groatsworth of Wit, bought with a Million of Repentance by Robert Greene (published September 20, 1592)
It would be nice if London hadn't burned to the ground in 1666, carrying off the state and company's copies of the approved books (which were pretty ancient by that time), because the 37 plays of the First Folio are the only complete texts that have survived. Cardenio survives as a single page of music with a dash of dialogue, and the unfiniished "Sir Thomas More" was a collaboration.