At a time, t1, if two persons, X and Y of equal cognitive and perceptual capacity, were placed one in one universe and the other in the other, I don't think there is a way for either to tell which universe, with a God or without a God, they were in.
But if we introduce temporal duration, the situation might be different. Here I merely scout a possibility.
If there is a belief in God in both universes (A and B), but God in only one universe (A), one would expect a belief in God to continue indefinitely in A since God would be the continuing author of religious experiences in A, experiences which would sustain a belief in God. What is to prevent a belief in God from dying out ? The fact that God exists in A and is the continuing author of religious experiences in A. Not all religious experiences need actually be real experiences of God, but some would be : and if all other religious experiences faded out, the real experiences would remain and so therefore would a belief in God. I assume you cannot have an experience of God without recognising it as such and hence believing in the existence of God.
In B, by contrast, there is no God. If religious experiences were to disappear in B, one could reasonably infer that there is no God because if there were a God then God would be the continuing author of religious experiences, experiences which would sustain a belief in God. No religious experiences, no God : a safe inference.
Note carefully that this is only meant to sketch a scenario, the persistence of religious experiences in one case and the disappearance of them in the other, which if were to occur would enable one to tell which universe one were in. If it didn't occur, then one couldn't tell. My point is simply that conditions are imaginable in which one could tell; those conditions might never be realised. My argument has no pretensions to go beyond that - to show that your question does not present an impenetrable wall of permanent ignorance as to which universe one is in. There are putative conditions in which one could tell.
This argument, lightly outlined, strikes me as more convincing than an appeal to divine miracles, since it seems to me impossible to tell whether a miracle has a divine or some other explanation or even whether a miracle actually has occurred or is merely falsely believed to have done so.
To anticipate an objection, I recognise that some religious will hold that God is the author of (some) religious experiences and that the genuineness of divine authorship of such experiences is self-evident : if they were in universe A the self-evidence would continue while it could not occur in universe B. I have no desire to enter into a dispute on this point. My reply is that for such people, the question above is not a philosophical question since it has been settled; it does not have the quizzicality of a philosophical question.