I came across an interesting theory named the McDonald’s theory. It is a trick that tries to motivate ideas in a group by first suggesting a bad idea. The theory sounds plausible because it would set a low bar of entry into a brainstorm. Co-workers may gain the confidence to start suggesting their own ideas because “nothing I suggest can be that bad”.
This trick does not address the root cause of the problem. That is, that people do not want to risk putting their professional image on the line to start brainstorming (i.e. risk sounding like idiots). We all want to excel at what we do so perhaps efforts should be focused on cultivating an environment where everybody feels like they are excelling. Unfortunately, cultivating such an environment may only be possible in the ideal world we don’t live in, but it should be tried for. There would likely be other benefits to such an environment such as improved morale– a sense of purpose driving employees work.
In regards to getting ideas to start: I think what will always matter is somebody needs to break the ice with some idea (bad or good). If you really want somebody to do that, then the person you can rely on the most is YOU.