The reason we "trust" science is that it has a stupendous track record. At least when we're wrong we can often show it! In other areas, except for dourly noting that history tends to repeat itself or at least rhymes (indicating that we keep making the same mistakes for millenia), we don't even know when we're wrong.

So if you are forced to make a choice, nothing has a better track record. (Of course, you should be careful to distinguish what people say science means and what the results actually are--people do their dastardly people-y things all the time.)

However, the whole point of science is that you don't trust it. You doubt it. You learn what seems to be known, understand why it seems like we know that, and keep asking: which parts might be wrong? How can we extend the parts which are right?

The state of society would be far healthier if everyone was more intuitively comfortable with this.