Woah, I'm surprised this hasn't been answered yet! Hey, maybe I can still help??
Using "Or" for a beginning word in a sentence is not really needed.
But I think it is possible in my opinion--
Ex: I'd like my applications turned in by today. Or, rather tomorrow is okay.
Though, it does not really flow well with the sentence and is ultimately looked over as an odd way to use your words. Maybe even it is considered technically wrong by English usage technicalities. I think the safest answer is to say "Or" should not be used in that order.