I suspect that you have been misled into thinking that Science has always been objective. Most scientists probably think they are being objective, but such isn’t the case.
An example is the very notion that the Newtonian “forces” were ever observed to exist. They were not. They never existed. But from a subjective standpoint, they seemed to exist and thus the “Laws of Newton” were established. Later, Einstein proposed a different ontological perspective concerning Relativity. Relativity directly states that ALL measurements are subjective (aka “relative to the observer”). And Relativity is very largely accepted as “Science” merely because experiments were done to substantiate the predictions. Quantum Physics gets very seriously subjective in claiming that reality itself only exists when the observer is conscious of it - shamefully subjective, yet Quantum Physics, an obvious fairy tale mythology, is strongly sold as “Science”.
The experiments themselves MUST be objective, but the proposed truths of the principles involved (e.g. Newtonian forces, Einsteins bending of spacetime, Schrodinger’s half alive cat) have always been subjective. Science can only tell of what is necessarily NOT true. It cannot tell of what IS true. The scientists simply don’t know enough philosophy to realize it (and certainly not the general public).
And that is the “science” part of anything called “Science of Ethics” - the objective measurements and experiments.
It might take a while to realize that gravitational force was accepted as a real entity merely because the resultant effects from experiments subjectively inferred that a force was involved even though there never was any such force. In a similar way, “The Science of Ethics” might presume that an ethical goal is that everyone wants to be happy (the “force”) and then provide the formulae involved. It might turn out that in reality, everyone doesn’t want to be happy (although that would be strictly an issue of definition), but that fact would not prevent it from being a science any more than the subjective presumption of Newtonian forces prevented Newtonian physics from being a science or the proclamation that all measurements and reality itself is subjective prevented Relativity and Quantum Physics from be “Science”.
There is a physics of psychology that might very well lead to a physics of ethics. Personally, I can testify that such really is true, but my personal testimony is not “science”.