The effort of gaining trust over an existing project isn't even really required. All you need to do is monitor when popular GitHub repos get archived. That's usually when the original authors don't want to work on it any more. Then just quickly make a fork to continue the project (think Phabricator -> Phorge), and if you're quick enough and authoritative sounding enough, boom control of the project!

Maintain it for a bit so people switch to your version, and job done.