I think overcoming death is how you awaken a zoan fruit. It being the final step
I made a thread a while ago on how I think characters like Kaido and Linlin were restricted by their own strength from getting stronger. Explaining my opinion on why they failed to awaken
Also the world government definitely knows a trick on how to force zoan awakenings. Them succeeding characters like Lucci/kaku, the gorosei, and now even shamrocks blade
The impel down jailer beast being failed examples