I had a head of HR (my bosses boss) who hated the phrase brainstorming, another colleague used to speak of such sessions degenerating into "blame" storming. And yet another colleague who was quite the introvert spoke of the existential dread of "having to speak up instantly in a group setting with everyone looking at the flipchart". I even had a client who despite a masters degree and being on a fast track hi-po program spoke of being "too shy to speak up in a room full of really experienced people".
Over the years I have been facilitating, these challenges have come up again and again, and one of the techniques I find most useful is "brain writing"
One person shares the problem statement / situation they are attempting to address, then
Each person in the group takes turns adding ideas for possible actions / solutions to the flipchart / whiteboard
As each idea is added everyone remains silent
Keep adding ideas for 3 or 4 rounds and only then
Discuss the ideas
Alternatively, after #1 above, you can use sticky notes or the digital equivalent in #2 with everyone coming up with as many solutions as they can (one solution per sticky note), then put all the sticky notes on the flip chart and then discuss / group ideas.