I suspect that pressure to believe in vagueness about the existence of material substances comes from a belief that facts about the existence of material substances supervene on facts about the physical arrangement of matter in the universe. The most plausible arguments for such vagueness is questions like this: What time t0 in the history of the union of the gametes of Bambi's parents is such that were the world annihilated at t, Bambi would not have existed? Given that the union of gametes is a physically continuous process, there seems to be an interval of time (perhaps several hours long) such that drawing a line at a particular point of that interval and asserting that it is precisely at that time that Bambi came into existence seems arbitrary.
But if one does not believe that facts about when Bambi came into existence supervene on facts about the physical arrangement of matter in Bambi's history, then an epistemic solution on which some particular point in that interval that we cannot scientifically determine exactly has the property of being such that Bambi came into existence precisely at that point is not that implausible. The fact that points slightly before and slightly t0 would seem to be just as physically fitting for Bambi's existence is irrelevant, since Bambi's existence does not supervene on whether there is a physical state fitted out for Bambi's existence. Compare the fact that when an atom decays at t0, it could just as easily have decayed shortly before t0 or shortly after t0—there is a real sense in which its decaying at t0 rather than shortly before or after (or maybe even a long time before or after) was arbitrary (unless Providence has some special reason for t0, which quite possibly it does). That doesn't trouble us that much, I suspect because we accept that when the atom decays is contingent. Well, likewise, if we accept that even given all the physical facts, it is contingent when Bambi comes into existence, we shouldn't be worried about the fact that nearby times are such that they would have done just as well as far as we can tell (though Providence might have some special reason for choosing one time rather than another).
The same issue comes up with regard to those like Trenton Merricks who believe in limited composition theories: some bunches of things compose a whole but not all bunches of things compose wholes. There seems to be vagueness as to composition. We can imagine a continuous sequence of hypothetical biological/physical situations, starting with what are clearly two trees and ending with what is clearly one tree (with in-between cases which, depending on whom you ask, look like two trees grown together or one tree with a bit of a divide down its trunk). It seems arbitrary to suppose that at some point in the sequence we have one tree, and very shortly before in that sequence we had two. But again, this intuition depends on a supervenience claim: the supervenience of facts about composition on facts about physical arrangement of matter. Granted such supervenience, we do seem to get arbitrariness. But why not, instead, deny supervenience, and simply say that what we get is contingency: given given a particular biological/physical arrangement of matter, there is a contingent fact whether all this matter composes a whole or not.
Of course one might worry about the Principle of Sufficient Reason (PSR) here. But if we believe in quantum mechanics (QM), then presumably we either think the PSR is compatible with QM or we deny the PSR. If we deny the PSR, then the problem that the story I gave is alleged to be incompatible with the PSR shouldn't worry us. But if we think that the PSR is compatible with QM, then I suspect that whatever story we give about the compatibility of QM and the PSR will also have an analogue here. (I defend the compatibility of QM and the PSR in my book on the PSR.) For instance, if we say that God providently chooses which otherwise random results of a quantum experiment will happen, then we can say the same here: God providently chooses when exactly Bambi comes into existence and whether there is one tree or a pair of trees. Or if we say that effects caused stochastically under probabilistic laws are not violations of the PSR, then we can say that there are probabilistic laws about the arising of substances or about composition.