We have all sorts of RCTs, blinded studies, placebo controlled studies, MR studies that look at genetics, meta-analysis, etc. etc. etc. that all support the causal link of cholesterol... I've linked literally dozens of these in the comments for this article. If you care, feel free to look at my recent comment history - it's all in there and all my claims sourced.

The OVERWHELMING evidence is that cholesterol is a hugely important causal factor. Overwhelming to the point that we can't do controlled trials for people with CVD risk with cohorts not on a statin in this day and age - it wouldn't pass ethical review, because we have so much data. It is not ethical to withhold lifesaving medication from people when we know it is lifesaving.