And the Higgs Boson became an “objective statement” only after it was verified. Prior to that, it was just a hypothesis.

We might have two different understanding of what it means for something to be an objective fact. Objective truth/facts/reality exist independently of human understanding. If all the humans got together and decided that the Earth is flat, that wouldn’t make the Earth flat. If scientists had never discovered the Higgs Boson, the particle would still exist.

Alternatively, perhaps you already agree with that and your point is more about the objectivity of statements (i.e., our linguistic acts). And while I disagree with your overall stance on morality, I can see the logic in insisting that our statements about the world be verifiable/falsifiable. Historically, some philosophers held that words that cannot be verified are literally meaningless.

So just to be clear, we can make a distinction between the objectivity of facts (e.g., physical facts, moral facts) and the objectivity (here, justifiability) of our statements about the facts. My stance is that there are objective moral facts. I concede the point that the justifiability of our statements about the moral facts is a difficult problem to solve. But finding the Higgs Boson was also difficult and we humans did it!