There is a distinction that you failed to discover, and thus your error. The distinction is ethics and morality. Morality emptiness the ego (Phil 2:5-8), and in turn God gives himself as wisdom (Sir 24:23-26, vulg.). Ethics is civic and embraces human secularism, it rules in only this world and is justified by a judgment of worldly perspective.
We came to pass morality to the poor and lowly, and in turn, they participate in the divine nature. (cf. 2 Pet 1:4)
You say: This means that any intelligent being, like human, can also justify it.
We say: Only the poor and lowly in the heart can do justice in moral terms. (cf. CCC 544)
You say: Humanity however does not agree on the fact that objective morality exists.
Yes, the rich in the pleasures of this world have there own wisdom - “for this is not wisdom, descending from above: but earthly, sensual, devilish.” (Jas 3:15) which is vain in the approachment to heaven. But useful in getting along. “And all that will live godly in Christ Jesus, shall suffer persecution.” (2 Tim 3:12)
You said: This means objective morality cannot be justified.
I say you have no grounds to state the case because you failed to understand the life of God and know what morality is. God does not inspire ethics. And I agree, there are no such things as objective ethics.