Your question is big. The answer I've landed on is little. We're just little furry wiggly wombly tubes struggling against the inevitable pressures of entropy. This is true down to the most basic molecule than can replicate.

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?"

Because when we get the opposite, our own behaviour has ultimately driven us into the ground and we end up in hell or dead.