From a game theory perspective, morality encapsulates behaviour that is viable over multiple interactions across long stretches of time.
Objective moral truths stem from that. The unending dance with entropy. To be the belle of the ball, we also harness that entropic randomness and turn it into dances that are even more powerful.
I feel the urge to thrive and grow and improve. I find myself sympathetic to the expressions of that drive from all life. That is a priori, that emergent empathy that many of us are capable of. I see a neighbor crying, a homeless man sleeping rough, a fearful stranger, and I say to myself, "There but for the grace of God, go I." But I don't stop there, because I see my puppy, I see a bird in the sky, I see a crushed mollusk, a writhing worm, "There but for the grace of God, go I." We're many faces, but still, we're all dancing with the entropy.
Next is the question, "Will this action increase or decrease the entropy in the universe? To the many faces, is this the action of an ally or an enemy?"
Finally, we realize we could superheat everything into crystals and reduce entropy that way. The last vital factor is the synthesis of order and disorder: complexity. These are the fun dances. Art. Learning. Creation.
So, to find objective moral truths, our sieve consists of The Golden Rule, "Am I fucking things up more?" and "Am I making things more awesome?"
Extremely stable societies are often marked by low social mobility and oppressive social mores, yet they fulfill every check mark according to your definition of good. It would also deem the emancipation of slaves an evil deed, since it disrupts a stable pattern of social order that's extended for a long stretch of time.
I don't know if I would deem something like ancient egypt, which had a social order that persisted largely unchanged for several thousand years, one of the most stable societies known in history (also an oppressive theocracy), I don't know if that is my idea of good.
Merely persisting is not sufficient for something to be moral, but it is a necessary requirement. We need principles on how to behave in repeated interactions and situations over long periods, or bad things will eventually happen. That's part of the purpose of moral truths you were raising a question about.
I'd just point out that ancient Egypt had developed moral-sensemaking technology that were state of the art at the time. It's the best we as humans could do to live in a large ecosystem and we're standing on their shoulders. It's not surprising that we would find fault.