Can you begin a sentence with "because"? Sure.
(You can begin sentences with "because" or "and" or "or" or "but."
You can even begin paragraphs with these words.)
I got up and turned around in my tracks three times and crossed my
breast every time; and then I tied up a little lock of my hair to keep witches
away. But I hadn't no confidence. [Huck Finn]
"It's over, Mr. Gates," says a voice. But how could
it be over? I had merely blinked. "You talked to us several times," the
surgeon had told me, and that was the scariest part of all. [Henry Louis
Gates, Jr., "A Giant Step," in The Norton Sampler, 4th ed.,
ed. Thomas Cooley (NY: Norton, 1993), p. 157.]
And yet . . . she had not looked in any way--as I
imagined the traditional `ghost' was supposed to do--transparent or
vaporous, she had been real, she had been there, I had seen her quite
clearly, I was certain that I could have gone up to her, addressed her,
touched her. [Susan Hill, The Woman in Black: A Ghost
Story (Boston: David R. Godine, 1983), p. 64.]
And so he performs from a distance, laughing at
his myth, throwing it away only to see it roar back and trap him once again.
[Greil Marcus, Mystery Train, rev. ed.(New York: E.P.
Dutton, 1982) p. 143.]