So if science is the empirical study of the universe, then the question of origins cannot be avoided. I'll rephrase my question: minus a First Cause, from whence came all this 'stuff'?

You missed out the all important qualifier "in a closed system".

The Universe could be infinite in time and space, in which case there's an infinite amount of entropy to draw on, and the observable Universe could draw on energy from elsewhere (i.e. the Universe may be closed, but the onservable part is not so) without any violation.

Pah! Postulate an infinite Universe? Let's postulate an infinite God instead! Universes don't set Rules of Behaviour, Dress Codes, Dietary Rules, and Laws of Sexual Behaviour, or any other useful levers of power.

So where did it all come from?

Science don't know. Science is trying to find out.
Religion don't know. Is Religion trying to find out?