It’s acceptable to begin a sentence with because or however, contrary to what many people learned. There is no grammatical principle to support the notion that it’s wrong.

Prominent writers have done it for decades, and language historians don’t know where the opposition originated. Because (usually a conjunction) and however (usually an adverb) are normal parts of speech that can appear in different places in a sentence. Because often appears at the beginning to add emphasis to that portion of the thought. However can begin a sentence to establish a contrast with something said in the previous sentence, or it also might mean in whatever manner.

Consider these examples:

 Because tomorrow is the deadline, I will need to work late. (adds emphasis to tomorrow’s deadline.)

Because no one had arrived, we left. (adds emphasis to the fact that no one showed up.)

Consider this sequence:

I like your idea.  However, we don’t have the budget this year. The word however will appear at the start to convey the contrast between the fact that it was a good idea and the fact that there is not sufficient money to act on it. 

Here is another, though less common, way that however is used at the front of a sentence:

However long I work here, I will want this office.

However you plan to proceed will be fine with me

In these examples, however means in whatever manner or by whatever means. No comma should appear after however in this context.

 There have been differing opinions on this topic among language commentators. Strunk & White encouraged people not to start a sentence with however unless it meant in whatever way. But they did not elaborate. One of their peers, former New York Times Editor Theodore Bernstein, said in his famous book Watch Your Language that “if your elementary school teacher told you never to start a sentence with ‘however,’ forget it.” He said to put however wherever you need to present the contrast, which is often at the beginning.

The contrast also might be necessary in the middle, as in I received many good ideas; however, I had limited time to read them all.