I think saying that a missing species is indistinguishable from extinct is better until and unless that is no longer true (one is discovered, say a coelacanth), in which case we change our position consistent with the new information. We go from being agnostic acoelacanthists to coelocanthists making us correct both before and after such a discovery.
The same method works for missing gods, that is, gods making no discernible impact on reality. They are treated as nonexistent until and unless that changes.
The difference, of course, is that unlike the coelacanth, whose nonexistence was falsifiable and falsified, the god claim is unfalsifiable if one also insists that the god, even if it exists, is not detectible.