I dont really see your problem - and would counter with "we cant understand the world without data, but we also cant understand the world with data alone"[1]. With your firstly and secondly you are basically just making the normative-positive statement distinction: Sure, you cant prove normative statements, that's the point! But you can learn more about them with positive statements, which you can falsify, verify etc.

People not accepting evidence is kind of not really a problem of science, but of science communication. But yeah, its also becoming an increasingly severe problem with examples such as climate change denial and anit-vaxxers on the rise

[1] hans rosling - factfullness