Telling average people to "trust the science" in practice means telling them to trust the guy who says "I am speaking in the name of science". Often, he is just lying. The average people are not going to "trust the science" by reading peer-reviewed studies.
Then there is the fact that someone can be a respected scientist in e.g. linguistics and simultaneously a crackpot in e.g. quantum physics, or vice versa. So you need to be careful even with trusting the actual scientists. (Similarly, the doctor talking about covid... is he an epidemiologist, or does he just fix broken legs?)
Trying to think about best solution to make the actual science accessible to average people... the "ask science" subreddit is probably the best currently existing option.
You don't even have to go that far. Scientists are just people. They are intelligent and experts in their fields but to be a Phd means you have a very narrow slice that you are an expert in.
The problem is when these people try to public support certain government policies. Knowing climate science or quantum physics does not qualify you to be a policy maker. It does qualify you to inform policy makers on your narrow area of expertise.
I've seen a lot of scientists pull appeal to authority fallacies by saying, I'm an expert in X and I say the government should do Y. Most people aren't scientists but they are smart enough to know that scientists don't know everything and usually not any more adept at politics or government than anyone else.
Politicization of science by scientists has done more damage to the public trust in scientific institutions than anything else.
Then there is the fact that someone can be a respected scientist in e.g. linguistics and simultaneously a crackpot in e.g. quantum physics, or vice versa. So you need to be careful even with trusting the actual scientists. (Similarly, the doctor talking about covid... is he an epidemiologist, or does he just fix broken legs?)
Trying to think about best solution to make the actual science accessible to average people... the "ask science" subreddit is probably the best currently existing option.