I don't think people who say "Trust the science" are saying that science has it all figured out. It's telling people that they should weigh scientific data into their thought process. In reality many people make all of their decisions based on emotions and "feels".

"Trust the science" really came into its full form during the pandemic and was a veiled line in appealing to authority. The CDC, Dr. Fauci, NIH, or any governing body issuing mandates during the pandemic would tell you to trust the science, when in reality they just didn't want people to question their decisions. As it turns out, some of the people questioning school closures or masks were correct! Questioning vaccine safety for young men was and is correct, as long as there were not comorbidities. The people or institutions that were yelling "trust the science" the loudest were indeed saying that they had it all figured out and that anyone that questioned them was wrong.

"Trust the science" became a campaign slogan during the pandemic, and fell into the same realm as "defund the police" or "trust all women".

So yes, "trust the science" does mean what you said that it is a process that should take data new and old into account. However, the sad thing is it was co-opted by people who used it as a cudgel to silence anyone that didn't toe the line.