But, it seems, the only people who say "no" to that question are neither professional writers and editors nor published authorities on correct style and usage in writing.
In other words, the correct answer to that question is "yes" ... or "yes, but ...."
The author of this recent article, by Allison VanNest at Grammarly, agrees and adds some good advice:
Feel free to start your sentences with “and,” the three-letter powerhouse of a conjunction – there’s nothing wrong about it. Just remember that the word “and” is grammar’s version of cayenne pepper; too much use can ruin the whole effect.I offer similar advice at Garbl's Editorial Style and Usage Manual:
and, but Some teachers wisely taught us not to begin every sentence or fragment of a sentence with and (or but). And others taught us mistakenly not to begin any sentence with those conjunctions. Whatever the lesson, the result has been a common misunderstanding that it's incorrect to begin sentences with conjunctions. Ignore that myth!
And and but are simple, clear and correct transition words between related (and) and contrasting (but) sentences. Go ahead and use 'em--And instead of Additionally, Furthermore, In addition or Moreover, and But instead of However.
But don't overdo it. They'll lose their punch. ...