Starting the introspective loop
It’s incredibly difficult to affect cultural change without top-down support, especially when it comes to introspection and deliberate decision making. Raising authentic feedback often challenges the status quo and is thus potentially risky for the person doing the raising. If it’s unclear how that feedback will be received, it’s safer not to raise it and thus it’ll go unsaid.
Leaders must make it clear that that feedback is welcomed, even if it challenges their current direction. I’ve found that a good place to start is narrating your own internal introspective loops for others, so that you’re effectively modeling the behavior you want to see in others. This definitely includes admitting your own fallibility.
As you communicate your decision making and strategy, you naturally invite a conversation about it. Welcoming that conversation, truly listening, and then narrating the outcome in a way that reflects the thought you’ve put into it shows your teams what you really value.
Clearly bottom-up support is important, too. All the space in the world for feedback means nothing if no one uses it. It’s unreasonable to put all the risk on folks without influence, though, so I’d start with trying to model the behavior from the top.