Regaining trust is IMO, impossible with all current politicians.
The government has basically designated the nuclear agency seat as a "Send the guy we don't like there" seat. Only incompetent idiots have been placed there since Fukushima.
Add in all the BS red-tape that the government made up, the notoriously slow bureaucracy, and sometimes even sabotage? (Combine that with the new nuclear regulation agency created after Fukushima, which complicates it further) It's not happening without a strongman leading the charge and really forcing it.
Would be great if we could copy-paste France's setup. But Japan is obtuse and inflexible.