As sentient beings, we have the ability to reflect on our own existence and consider the moral implications of our actions. But what gives us the right to exist in the first place? Is it simply the fact that we are alive, or is there a deeper moral justification for our existence in the universe? What are the ethical considerations that arise from our place in the world, and how do they shape our understanding of ourselves and our place in the universe?
Your question incorrectly assumes we need a right to exist. A right is a human invention- it is something that is defined, conferred, recognised or denied by people. Matter generally, of which we are composed, does not need a right to exist. Life has evolved as a consequence of the way in which the fundamental particles of matter interact in our local (in the Universe) environment- no permission or moral justification is required for that to happen. Indeed, questions of morals and ethics are again human inventions, so to ask whether human concerns justified events before the existence of humans is an absurdity.
Ethics too are matters of human judgement and opinion- they are not absolutes. What you consider to be ethical is a consequence of your upbringing, education, patterns of thought and so on.
There is no absolute moral right or wrong. It is up to humans, collectively and individually, to determine which ethical issues are important.
My own view is that the key ethical questions are those to do with Earth and humankind as a whole. For instance, to what extent do the humans alive today have a responsibility to act to benefit humans in the future? Assuming the Earth has a limited capacity to sustain life, should we as a species make efforts to allow other forms of life to coexist with us or just maximise our share? Is it right that so much of the world's wealth is in the hands of such a small percentage of the world's population? Is the idea of nationhood becoming unfit for purpose? What should the developed states, which have become rich by abusing the resources of the world, now expect the developing states to make sacrifices to combat global warming? And so on.
One established author who's addressed this question is Nicholas Rescher, in his book Axiogenesis. He has a somewhat peculiar argument on behalf of this world being intrinsically good and even, provocatively, optimal. He parses, "Why is there something instead of nothing?" as, "Why are the things that are, the particular way they are, and not some other way?" Then he uses (strange, but considerate) reasoning to promote his optimalism thesis.
Environmental ethics also involves discussion of such topics. Generally, there are puzzles in deontic logic concerning the difference between "ought to do" and "ought to be":
... OB-NEC [as a] rule requires that any tautological statement is obligatory. Now consider the following statement:
(1) Nothing is obligatory.
It seems that what (1) expresses, an absence of obligations, is possible. For example, consider a time when no rational agents existed in the universe. Why should we think that any obligations—even those pertaining to tautological states of affairs—existed then?
If we are reading OB as simply “it ought to be the case that”, it is not clear that there is anything counterintuitive about OB⊤ (now read as, essentially, “it ought to be that contradictions are false”), but there is also no longer any obvious connection to what is obligatory or permissible for that reading, or to what people ought to do. A different way of avoiding the counterintuitive consequences of OB-NEC is by distinguishing between “vacuous” obligations such as OB(p∨¬p) and those that require the satisfaction of some logically contingent statement such as OB(p&¬q). This can, e.g., be done by enriching one’s language with a modal operator □ for “settled true” (cf. Belnap 2001 et al., Horty 2001).