Let us consider a much reduced version of the problem of evil, or the question of a god’s/supernatural powers (e.g. prayer healing) in the world: that a benevolent god, who acts according to well-defined lawful aims, has the power to change an individual’s mind, or to modify DNA, or other similar small-scale physical manipulation: but that this power only can be exercised very infrequently.
The ability to change one person’s mind could prevent nuclear annihilation, so the avoidance of such clearly is consistent with said existence. Given the stochastic nature of the spread of viruses and bacteria, at some level this also could be said to be consistent with the existence of this entity.
Now, consider how we attribute actions to this god, vs. the actions that this god has not influenced. The vast majority (99.9999%+) of mental states, and the vast majority of biological/chemical reactions, are not even remotely observed at such a small level. We assume that what we do observe is indicative of the entire physical reality under those set of conditions, but we never can measure this. In the case of mental states, even if we consider that an individual does have conscious perception and rational undertaking, that is not observable to others – and we all know many people make mutually exclusive claims about gods and prophets.
So the first problem is: we observe an infinitesimally small fraction of this distribution; therefore, we cannot make any statistically valid or reproducible claims about it, beyond its apparent convergence to the macro physical reality that we do observe on a regular basis. Neither mental states, nor the evolution of pathogens (or anti-pathogens) are bound to this physical reality: mental states of course, but flipping/inserting/removing some nucleotides in DNA is a very localized operation, and as noted the vast majority of mutations in organisms never are observed. Because we cannot know the vastly easier to find and characterize notional bulk of the distribution, which, for simplicity, we (not necessarily correctly) assume would obey some physical or stochastic principles, we have no way to characterize the distributional shift towards good outcomes induced by this god’s actions.
Consider then the strategy of this god: the god is omniscient, benevolent, but only has a few cards to play. What if this god has to deal with the Nazis? There may be too many minds to change. The better alternative could be biowarfare – but that may not be an available opportunity. What if this god only can change nucleotides? Then, if this god knows the next Hitler has been born, this god may have to cause a horrible cancer, or even start a pandemic, to kill that Hitler, saving a net of millions of lives. Consider instead: if this god only can change minds, and knows that these humans are willing and capable of initiating horrible biowarfare and other torture on the whole of humanity, if they are allowed to progress to a certain technological or cultural state. Then, it may be that this god must deliberately cause humans to wage war on each other, to prevent this process from completing.
Hence the problem not only is about measurement, it is about the significance of the measurement, even if you knew exactly which actions this benevolent god took. Without your own omniscience to know that this god’s actions killed the next Hitler, you have no means to distinguish a viral mutation from a benevolent god vs. a devil.