You can't build trust over science, that's just an error of category. You can only build trust in some people on some topic. One can measure reliability in a process, but if no specific human is involved, there is no literal trust engaged.

Now of course, to each its definition and metaphors are useful tools.

But when one starts a discussion on truth, trust or reality as core topic, it's better to start with what is meant with these words and in which context to which scoped boundaries.

Because of course, science can back a contemporary etnologic account that asserts there is no (longer) different races in homo sapiens, just as much as it can serve as frame for phrenology and whatever supremacism claim.

So no, we didn't build trust in science over centuries, and not even in any scientific person because we don't have that much humans to hold the role of such a trustable entity over such a long period of time.

Social institutions can carry unchanged names over centuries, but that tells nothing about how trustable are the people that inhabit them over time.

LLMs certainly come with their own challenges, but the erosion or scientific institutions with its bizarre scheme of publication process have been there basically as far as I can remember.