No. Car is similar to parce que, but it's a coordinating conjunction and thus cannot begin a sentence or clause.
Why wouldn't it be a sentence? Surely you aren't the kind of person who would reply to "Why did you make breakfast for me this morning? You didn't have to do that." with "I made breakfast for you this morning, even though I didn't have to do that, because I love you."
Of course not, you would just say "Because I love you." which makes it a sentence just like anything else.