there are several ways ~objective morality could exist:
1) our emotional reactions to classes of actions fall into some attractor basis which exists cross species. this would be emotivist (quasi-realist technically) compatible, and anti-realist since moral statements technically still ground in stances (emotions). but if this evolutionary attractor state existed, we could expect ~universal overlap in moral sentiments. not technically objective, but close enough. (to make this have "normative force" you'd just have to pair this picture with a single non-natural moral axiom: what is good is what evolution nudges us to robustly prefer. this might be the flourishing of all conscious creatures (it's possible enlightened consciousnesses converge on this non-natural intuition. agopic love, jesus, the buddha, etc)
2) physical reality is but the tip of the iceberg of reality, of all that can be said to ground true objective facts. there may be a mathematical "realm", normative "realm", and/or a moral "realm". "realm" is a horrible world since it feels spatio-temporal, but this analogy is misleading. these "realities" are better thought of as "latent structures in overall reality". these are Platonic Forms (form = structure). we discover truths about these realms via reason. this is not spooky, we do this with math, logic, an modal truths all the time. moral isn't that much weirder
3) morality is grounded in patterns in valence of consciousness. perhaps consciousness is structured in a way where all conscious creatures, necessarily, perceive things as Good or Bad. maybe this doesn't get you "duties" and "rightness and wrongness", but only Goodness and Badness. but this is still a moral domain where objective statements may be made (there are facts about whether, how much, and why someone is experiencing positive valence rn. this is true even with emptiness). that's sorta objective morality if you squint
4) some truths are known with brute intuition with no further grounding. they're just undeniable with clear thinking. examples include: "more of something good is better than less of something good, all else equal" or that "suffering is bad, all else equal". these are not definitionally true, but obvious in the same way that modus ponens is. this is Parfit and Scanlon's take
5) morality is just game theory: this would make non-naturalism make more sense ("get the highest payoff" as the one universal moral norm) while also being rooted in natural facts (the player's actual, psychological payoff schema)
I don't understand how morality can be objective. morality arises inside the human mind. you could derive facts about "universal human mortality" that almost everyone shares, like how almost everyone has 10 fingers, but this is a character of humans, not a stand-alone fact