Maybe not, maybe there is an infinity of variation of objective morality. There will always be broken people with pathologies like sociopathy or narcissism that wouldn't agree. But the vast majority, like 95% of people would agree for example on the universal human rights - at least if they had the rights and freedoms to express themselves and the education to understand and not be brainwashed. Basically given the options of a variety of moralities and the right circumstances (safety/not in danger, modicum of prosperity, education) you would get an overwhelming consensus on a large basis of human rights or "truths". The argument would be that just because a complex machine is forever running badly, that there still can be an inherent objective ideal of how it should run, even if perfection isn't desirable or the machine and ideal has to be constantly improved.
There is another way to argue for a moral starting point: A civilization that is on the way to annihilate itself is "doing something wrong" - because any ideology or morality that argues for annihilation (even if that is not the intention, but the likely outcome) is at the very least nonsensical since it destroys meaning itself. You cannot argue for the elimination of meaning without using meaning itself, and after the fact it would have shown that your arguments were meaningless. So any ideology or philosophy that "accidentally" leads to extermination is nonsensical at least to a degree. There would still be an infinity of possible configurations for a civilization that "works" in that sense, but at least you can exclude another infinity of nonsense.
"Who watches the watchers" is of course the big practical problem because any system so far has always been corrupted over time - objectively perverted from the original setup and intended outcome. But that does not mean that it cannot be solved or at least improved. A basic problem is that those who desire power/money above all else and prioritize and focus solely on the maximization of those two are statistically most likely to achieve it. That is adapted or natural sociopathy. We do not really have much words or thoughts about this and completely ignore it in our systems. But you could design government systems that rely on pure random sampling of the population (a "randocracy"). This could eliminate many of the political selection filtering and biases and manipulation. But there seems very little discussion on how to improve our democracies.
Another rather hypothetical argument could come from scientific observation of other intelligent (alien) civilizations. Just like certain physical phenomena like stars, planets, organic life are naturally emergent from physical laws, philosophical and moral laws could naturally emerge from intelligent life (e.g. curiosity, education, rules to allow stability and advancement). Unfortunately it would take a million years for any scientific studies on that to conclude.
It is quite possible that it's too late now, or practically impossible to advance our social progress because of the current overwhelming forces at work in our civilization.