I would distinguish between truly natural evil and unnatural physical evil.
Evil, in the most reductionist definition of it, simply refers to the absence of being. Its “existence” is necessary for the positive existence of any finite creature, since without absence of being “surrounding” so to speak the existing being in its finite perfections, every perfection of it would be infinite and it would not be a creature at all but God. If God was going to make a creation at all this kind of natural “evil” was necessary, and it was not wrong for God to allow such absence to remain as he has no duty to fill it.
What you mean, though, is absences/limitations that violate some aspect of nature. Obviously prior to creatures with free wills no such evil can exist, because everything else comes directly from the sovereign Will if God. Only with the choices of free creatures coming into the picture can you get something that violates the natural order instituted by God.
A free choice that violates the natural order is a moral evil, but because we free creatures can have an effect on the physical world morally evil choices can cause events to happen in physical creation that violate the ordaining will of God.
A simple example would be one man murdering another with a knife. Everything with objective being in this picture, each of the two men, body and soul, and the physical knife, are good in the positive existence they have from God. The primary evil is the decision of the murderer to murder (to seek some lesser good in preference to the greater good of justice towards the murdered man), and the secondary evil flowing from this primary evil is the wound inflicted by the stabbing. This secondary evil is physical rather than moral, though it has resulted from a moral evil.
Since God is good and would not introduce such disorders into His creation, we believe that all such physical evils result in some way from moral evil, even though the connection can often be harder to see.
I, for one, find the idea that there would have been no physical injury to or death of biological organisms before the Fall entirely unconvincing. If there were anything wrong with such injury or death we would have to starve ourselves, since we as human beings need to consume other living things to survive. There is no question of moral evil in the case of non-human animals, yet they also need to eat other organisms to survive. There are scavengers, but where would they get their carrion without other animals dying? Then there’s all the fossil and genetic evidence for death and the passing of generations before our species emerged.
Certainly logically possible ways to get around these sorts of objections can be found, but I see no need for it. There is nothing I at least can discern to be wrong with nature as it exists apart from humans. The problem comes in when human beings are subject to the same kinds of suffering and death that other animals are. This is an evil, but one we have always believed happened after and as a result of the Fall.
Adam and Eve were given “preternatural gifts” which among other things protected them from illness, aging, and death, but which were somehow tied to their original justice, such that when they sinned they lost both those preternatural gifts and the ability to transmit them to their offspring. As a result we are subject to the same kinds of decay and harm to our bodies as other biological organisms, and what was good and ordained by God for them becomes an evil when it affects us.
Thus a hurricane, for example, would have been an unadulterated good if the fall had not occurred, but with our new human frailty it now becomes a physical evil.
One final note, as a result of the fall we often also have difficulty distinguishing good from evil, which may also result in a perceived evil that is not objectively there. Thus, some people will be horrified at, say, predation or parasitism or decay in nature despite its objective goodness. In this also may be instinctive self-preservation (don’t eat the rotten meat, don’t touch the intestinal worm, keep your distance from that spider or lion, etc.), but this would not have been necessary or rational for us before the fall.
