ultimately all concepts are human creation, so they're subjective, but I think the vast majority of people have a general idea what morality is (not the exact rules, but the end goal) and this general definition can be considered functionally objective in the same way we can "objectively" say a tree is a tree, but if you wanted to split hairs, you could say it's subjective like all language and many many commonly accepted concepts don't have very precise definitions and they changed over time (e.g. I'd say it's way more difficult to talk about "nature" objectively existing than morality)
morality determines which actions lead to the creation of a perfect world i.e. a world without any (or minimal) suffering (and I don't mean just short term hedonism, suffering can be created for long term reduction of suffering, details are debatable but the general goal is as "objective" as a concept can be i.e. commonly agreed upon and has a biological basis)
some people will say "suffering is ackshually good" but it's because they think about suffering for a greater cause or sublimating the suffering into a greater pleasure (like masochism) and I'd cover it under my definition
if you split hairs about the precise definition, definitions changing or edge cases, you'd have to admit everything is subjective i.e. "animal" is originally something "animate" but not only we have plants which move (not just basic movement in the direction of light) but we also have animals (oysters) which don't really feel and only move thru simple mechanisms like plants or not at all, and obviously now we have robots and AI which may cover many characteristics of an animal on surface level but they're not considered such - if animals objectively exist, so does morality imo
There are no objective ethics without God.
I get the general idea of suspecting God would be the best source of morality, but I wouldn't agree it'd be any more objective than "godless" morality for many reasons:
- in practice, there's no way of knowing God's will (or even if one God with precise moral rules exists), so ultimately you're depending on your interpretation of selected Scripture, the opinion of selected "representants" of God or just straight-up your own "revelation" which is still just choosing your own morality (you choose/create your image of God)
- not only God's will can't be known in practice right now, it can't be truly known ever: even if a hand of God extended from the sky and he gave us a list of rules, you can't ever know if it's not just a trick of senses (hallucination), a "magic" trick (forgery using technology or otherwise, i.e. Project Bluebeam) or even, if you're religious, a false supernatural entity pretending to be God, Christianity warns of false prophets who will do miracles
- "objective" means "independent of mind" and God is obviously a mind, in the end we'd depend on his opinion which you don't really need to agree on (even assuming he's flawless, but that can't be verified either, so you potentially can still deal with a flawed being); considering "immoral" actions are possible, morality always needs to be subjective in the most strict sense, otherwise it'd just be a law of physics (which itself is objective but again you have the epistemological issues from point one, so our knowledge of them isn't truly objective (but I'd say it's "objective enough", like with morality it makes a sense to make a leap in logic))
- it's an extension of point three, not a logical one but more practical one, but many people could consider God to be evil (or just to have imperfect morality) by their own standard, it's even the case right now with many people seeing God's guidance in Old Testament flawed -- of course, morality isn't a democracy, but how we'd establish God's morality as superior over these people? is it because he's the most powerful, knowledgeable or he's the creator? none of these characteristics say anything about his morality (and until we can objectively establish God's will (which will never be possible per point 2) should we assume powerful, knowledgeable people or parents are morally superior?): you can be powerful and be evil (in fact, it's common), you can be knowledgeable and be evil (in fact, it's common) and a creator (i.e. a parent) can be bad towards his creation (in fact, it's common) -- the only way out is assuming God is good (the source of all good etc. ) like most religions assume, but that's circular thinking "God is good because we assume he's good", it won't convince anyone who's not already convinced
of course, you can assume to know God's will and use a less strict definition of "objective" or see God being the ultimate source of morality as an axiom etc. but from any other perspective than your own, it's still completely subjective