Is it Correct To Start A Sentence With a Coordinate Conjunction [duplicate]

Solution 1:

Yes: in fiction.

No: in formal/academic papers, or in many non-fiction books.

Thomas Pynchon is one of the greatest American novelists and a great stylist. You'll find in his work:

"Bigger, not softer, ése. And speaking of lunch, how about tomorrow at Vineland Lanes?"

Zoyd had played a few mob weddings in his career, nothing the kid couldn't handle, and besides the eats would more than make up for any awkward episodes, so it wasn't as if he were running a mean trick on his daughter's boyfriend, whom he was still not 100 percent crazy about, or anything like that. And as a problem to be addressed, Isaiah was more like a vacation from deeper difficulties, chief among which, all of a sudden, was the recrudescence of Hector Zuñiga in Zoyd's life, a topic, as he lit a joint and settled in front of the soundless Tube, that his thoughts unavoidably found their way back to.

Vineland, by Thomas Pynchon

Also, see:

A Grammar Book for You and I-- Oops, Me!: All the Grammar ... C. Edward Good - 2002 When you exercise your new writing muscles and use conjunctions to start sentences, make certain you do not put a comma immediately after the conjunction.

the section that starts with

Never Start a Sequence with a Conjunction Poppycock, on p. 157

which includes comments from the great stylists of the past, such as Fowler and Follett.

The most exhaustive essay on the matter that I know is:

Garner on Language and Writing: Selected Essays and Speeches of Bryan A. Garner By Bryan A. Garner. See: On Conjunctions as Sequence Starters at p. 63

Garner being the preeminent style expert of our time, IMO.

I'd strongly suggest to at least peruse it.