The notion that the universe was created or uncreated is not falsifiable, and thus not scientific. Science cannot say that the universe was definitely not created by a deity.
Science can say that the Big Bang or life itself did not need a creator in order to come about. Occam's razor comes into play here, since a complex creator at the beginning of time is much more unlikely than not, given that the complexity we observe came about as the result of a time-dependent evolutionary process (nothing complex was possible until the universe cooled).
The supernatural is always a possibility when there is no other plausible naturalistic explanation (proven or not). I don't say that evidence for a deity or other supernatural thing (or their necessity as a means of explanation) will never be discovered, only that up to this point, it has not.
The state of science as it is today does not support or require the intervention of a deity.
I think the function of mystical thinking is to exercise and challenge science in order to assist in it's growth and discovery.