The notion of extinction doesn't really show up until the late 18th century or so — Georges Cuvier is generally credited for making the notion a serious concept that was taken seriously.

To believe extinction is possible, you need to believe that the supply of animals/plants in the world is in fact exhaustible, and to do that, you need some way of actually seeing that in at least one case, you didn't just kill all of the deer in a single forest, but you killed all of the deer. Prior to solid footing in areas of taxonomy (so you can tell that a deer is a deer is a deer wherever you are going) and cases where you know the geographical limits of a species (such as the dodo, where they just aren't anywhere else than where they had been), and good records that show that the species that was supposed to be extinct actually existed in the first place (there are a lot of nonsense animals in early zoological catalogues), it's hard to establish that extinction is a thing.

If you have a belief in the world that also assumes that animal populations are divinely proportioned, and that natural resources are infinite, etc., that makes it doubly hard. (I don't know about the Ancients but this was definitely the case with Christianity.)

As for discussing "potential consequences" — this is an example of ecological thinking, which is also relatively recent. This requires you to see the world as essentially interconnected on a biological and material level in really direct ways, and that does not get established until the 18th century either.

As with almost all things, you can probably find isolated examples of this sort of thought in the writings of one Ancient philosopher or another, but to my knowledge none of these notions were dominant in any of the major philosophies going around at the time, and were not dominant in Western thought until much later. I do not know about Eastern thought, other forms of thought, etc.