Universe eternal or ex nihilo

It seems to me that, apparently, there are two possibilities accounting for the existence of the Universe: it is either eternal, and if so, it has only been changing shapes eternally (Big Bang being only an episode in its history); or it came into being ex nihilo. Does science promise to give a self-contained explanation of either? Or is this question, in the words of Richard Swinburne, an Oxford professor of philosophy, too big for science?

Response: Science can never explain why science works, or why the particular laws that science discerns should apply rather than other logical possibilities.