Can "anyways" be used at the beginning of a sentence?

Solution 1:

From Paul Brians’ book named "Common Errors in English Usage":

“Anyways” at the beginning of a sentence usually indicates that the speaker has resumed a narrative thread: “Anyways, I told Matilda that guy was a lazy bum before she ever married him.” It also occurs at the end of phrases and sentences, meaning “in any case“: “He wasn’t all that good-looking anyways.” A slightly less rustic quality can be imparted to these sentences by substituting the more formal anyway. Neither expression is a good idea in formal written English. The two-word phrase “any way” has many legitimate uses, however: “Is there any way to prevent the impending disaster?”

So you may prefer using "anyways" colloquially but "anyway" is a more formal way.