Cochrane is an important potential ally to EA. I'm technically a Cochrane author after being part of a team that submitted a review protocol, though I haven't been closely following their work over the past couple of years. Cochrane has traditionally been strong on evidence-based medicine and treatments, i.e., drugs. They have expanded in recent years to cover other important topics as well.
The typical Cochrane review is first proposed by a team of researchers in a protocol. The protocol is considered by a Cochrane Review Group (https://www.cochranelibrary.com/about/cochrane-review-groups) and moves forward from there.
The general public may be able to participate through various crowdsourcing efforts managed by Cochrane. A quick summary of those ways to get involved is here: https://www.cochrane.org/join-cochrane
The Cochrane Handbook is a great resource on evaluating research evidence and conducting systematic reviews. It is available online: https://training.cochrane.org/handbook