In order for NO death to have existed prior to sin, all animals, and all plants, all bacteria, all fungi, all protists, everything would have to also not reproduce (In the new Earth where we will be eternal, we will no longer reproduce, because of this constraint, reproducing without death into infinity.. think about that). But the first commandment from the Lord was "Be fruitful and multiply" and the second commandment was Genesis 1:30.
Let's make sense of this. Death had to exist in some form, because otherwise the entire planet would be completely overrun, complete overpopulation. It did not exist with man, and note that they did not reproduce until after the fall.
Second, if it was impossible for anything to die, why did they have to eat? What would happen to them if they did not eat? Would an animal not starve to death if it just neglected to eat?
Why did Adam and Eve have to eat the fruit from the tree of life?
The explanation to me is, that the tree of life enhanced cellular division in a way that prevents aging and probably prevents sickness, and probably heals from injury rapidly, so that as long as you ate it, you would not die. But without the fruit of the tree of life, the body begins to fail, and will eventually die. Genesis 3:22 indicates that even with sin, if man had continued to eat from the tree of life, they would live forever.
Genesis 1 never mentions the creation of fungi and bacteria but they exist, and seem to be designed to recycle dead organisms.
So ultimately, the bible does NOT ever explicitly say that animals never died before the fall, within nature we have organisms specifically designed to process death, and we have a finite space where infinite reproduction with no death makes no sense and these animals had a biological need to eat and food was provided for them, which indicates that if they didn't eat, they'd starve.
Mankind lived forever because of the fruit of the tree of life, after man sinned God cut him off from the tree specifically so that he would not eat it and live forever, since then, man has died.
If you want to convince me that a finite sized planet was to have infinite reproduction without death, and that animals would not starve if they did not eat until Adam sinned, you're going to have to show me scripture where it specifically and explicitly states animal death did not exist prior to the fall. Animals weren't eating the fruit of the tree of life, so to me, that would lead to the possibility of them dying.
Now before Romans 8:22 is pulled out with a leap of logic to claim that means animals were immortal before Man sinned, of course all of creation groans, animals could maybe die of old age, and possibly injury or starvation before the fall, but it was made so much worse after the fall. Many argue that predatory animals did not exist before the fall, after the flood they absolutely did though, and do, and I would think that perhaps pathogenic bacteria and viruses did not exist prior to the fall either, the ground and creation were cursed when Adam sinned, competition for resources probably became much more tight, things could get infected with diseases, food might not grow because conditions became more hostile. It's not necessarily an all or nothing picture that is painted. That is an assumption people make in their interpretation. After the earth is made new, and there is no curse, that competition for resources won't be so fierce as things will grow readily.
Actually that makes me wonder though, in the glorified bodies, would we still need to eat and drink, we'll have the fruit of life available, but if someone would stop eating it for whatever reason would their body fail and they'd die physically?