To answer the second part of your question first-- there was no question about the validity of Shakespeare's work during his own lifetime. Nowhere, across all the letters and treatises and witty prefaces to plays of the period, did any contemporary insinuate that Shakespeare was a fake or a pseudonym or anything but their friend Bill from Stratford. In fact, he was praised for his talent and mocked for his lack of education by Ben Jonson, "[Shakespeare] had small Latin and less Greek."

Not too long after his death, the theatres were forced to close during the English Interregnum period. When they reopened, Shakespeare didn't disappear, but styles had changed. While his plays were adapted into proto-musicals and other entertainments near the end of the 17th century, Shakespeare the playwright lost significant popularity. But, his gravity in the realm of English Literature was soon to explode again. (Capital R) Romanticism saved Shakespeare from the eternal limbo of mediocrity and anointed him 'The Bard'.

This image of Shakespeare as 'The Bard' and recognition of Shakespeare as the greatest writer in the English language was the work of the Romantics. Around 1800, writers and readers found exactly what they were looking for in Shakespeare: tragic heroes who spoke in ornate poetry about love and death and adventure and everything else people appreciate Shakespeare for. Along with this reputation for skill came doubters and, here, we arrive at the question of authorship.

Some point to an early literary critic/theorist James Wilmot as the first to question Shakespeare's validity. In the late 1700s (150 years after Shakespeare died), Wilmot set out to write a biography of Shakespeare but he was surprised by what he came across. Instead of finding lots of letters in Shakespeare's hand and manuscripts of plays or other writings, he found almost nothing like that. A few signatures on a house deed or marriage certificate, and nothing more. The Anti-stratfordians [those who deny Shakespeare] will be quick to point out that these signatures don't even match.

Wilmot's findings lay the groundwork for much of the anti-stratfordian argument as it has existed for the last two hundred years. The argument is rooted mostly in classism. "There's no way that this son of a glove maker who never went to college and left behind little evidence of his writing manuscripts could've been THE BARD!" People didn't start suggesting alternatives until the early 20th century, some people like Francis Bacon as Shakespeare, some find promise in the Earl of Oxford, I'm particularly partial to the ludicrous theory that Shakespeare was a middle eastern man who moved to England and that "Shakespeare" is an anglicized version of his real name- "Sheikh Al-Zubair."

You say you don't need debunking, but please, let me just have the chance to impart that these theories are all fabrications. And stupid ones, I think. The Anti-stratfordians seen interested in further romanticizing the Shakespeare story, but isn't the story we have more romantic anyway? The son of a glove maker who used the tools equipped to him by his public school education to write the greatest works in the English language and retire to a comfortable and simple life in Stratford-upon-Avon. He was a Craftsman who wrote to make a living and managed to leave behind something pretty special. I'll stick with that story.

Here's a few answers I dug up. This is just what came up on my quick search. There may be newer answers or more to be said.

"Is there any solid evidence that Shakespeare's works were written by others?" by u/texpeare

"Do you think Shakespeare actually wrote the famous plays? What do the experts think on the conspiracy?" by u/BigKev47

You could also check out r/ShakespeareAuthorship.