... we don’t know if it means anything to say that something exists “outside of space and time”.
We don't? Now, we might not know how to check if something is nonspatiotemporal,D but this is not to say that we don't have a clear enough general sense of the description. There are at least four families of theories about category mistakes, including three subtheories that turn on the difference between meaninglessness, lack of content, and lack of truth-value, and allowing for nonconceptual mental content on the one hand, and denying truth-conditional semantics on the other (not a stretch, since questions and imperatives have semantics but aren't (usually/directly) truth-apt), we find that we should be cautious in saying that "not spatiotemporal" is entirely void of possible significance.
Per the overall issue, here, though, the SEP article on divine hiddenness and a counterpart IEP article address reasons why a deity might "have reason" to hide itself, as well as objections to these supposed reasons. Immanuel Kant ominously claimed that knowledge of God would undermine the integrity of our will before the tribunal of the moral law, though his claim's viability perhaps then depends much on his (unnecessarily) rigoristic sense of that law (he argued, roughly, that if we knew of God, we would always do what is right, but out of fear of punishment, an impure motive in his eyes).
Upshot: if a realistic (but what would that even mean?) definition of God deductively led to this God having a reason to not hide Itself, then the absence of God's not hiding Itself would be evidence of absence of God in the first place. Kant's concern seems moot, actually, though, insofar as he also claimed that it was impossible for God to prove Its existence to us anyway, so the scenario he fretted about is either irrelevant because (not-ought)-not-implies-can,C or because if we knew God to exist, the metaphysical conditions giving rise to the moral law (the ought-would distinction in practical reasonW) would not obtain and there wouldn't even be a moral law to undermine in the first place, either, then.
DTo be very precise, we must first ask whether it is possible to differentiate zero-dimensional spacetime from not spatiotemporal at all. If not, then saying that God is not subject to spacetime mereology at all is just to say as much as that God is a zero-dimensional "dot" embedded in no other coordinate system. (C.f. Nicholas of Cusa's "sphere with its center everywhere and circumference nowhere.") And yet another option would be to not deny that God's intrinsic presence is in some kind of spacetime, but to say that this presence is in a maximum possible number of dimensions of this (c.f. Kant's God as the "engineer of dimensions"). With Augustine and Anselm we might go ahead and say that the number is infinite, with Cantor even absolutely so. This picture is radically underdeterminate, granted, but this is not the same as for it to be meaningless, lacking in content, or without truth-value.
CSo if God can't make us know Its existence by intuition, then there is no moral fact of the matter, for us, about what it would be like if God could do that (again, per impossible).
WKant says that, "I ought..." means, "I would, if reason was the only determining ground of my will." Kant is happy, as many theists are, to claim that God can be the greatest being, morally-speaking, without having to "build Its soul up" like in aretaic theodicies, which Kant himself half-replicates with his immortality postulate and his imagery of "crucifying oneself" (in the Religion). This, then, because God is such that Its "oughts" are actually already Its "woulds." The reality is, then, though, that if we knew God to exist, we wouldn't fear punishment from this being, since we would know that this being wouldn't absolutely punish us. Besides, the transformation of the physical world accompanying the intuition of the divine nature being imparted upon the creation would change the playing-field, so to speak, so that motives for certain kinds of offenses would presumably often be altered, too (why kill when you know God will resurrect all living things or maintain them in noumenal immortality regardless?).