If time is just a by-product of our physical universe, then anything that happens instantaneously (quantum non-locality) is in a sense happening outside the box, or outside our reality. So while one cannot know that there is something else more fundamental which exists outside our physical universe; i think there is observable phenomenom which indicates it is possible. And whatever the nature of this extra-universal thingy (one might call it a platonic realm); its not constrained by our sense of time hence it may be in an infinite state. So while infinity does not exist in our universe, it may do outside it. So one might ask whether a BB or BH singularity actually exists in our universe, our does it actually represent this unknowable infinite and platonic realm?
So going back to the OP : "Can empty space or emptiness conceive a form from which matter arise? "
I associate your idea of emptiness with my belief in an infinite platonic realm, so i certainly think something can appear out of nothing, but it did not really happen out of nothing. But because its source is not in range of our reality and timeframe then we cannot know it to be true for certain. Scientists stop at the singularity, no doubt FAPP>