so to remind and clarify a few things:
The way he got his powers is entirely illegal and actually considered a pretty serious crime. He didn't report the dungeon when it showed up, he entered without a license and he cleared it. Clearing dungeons in particular is a pretty serious crime as that eliminates a national resource. So explaining how he got it is a no go.
Showing his powers doesn't work either as, as far as he and everyone he's encountered is supposed to know, his abilities shouldn't exist. Officially, you aren't supposed to get anything from the magic metals from black dungeons and those that know otherwise never saw anything like this before. He would be assumed to be a shapeshifting monster before they believe he's a person that actually got something like this from there.
Lastly, mc and everyone else isn't aware that his mana is anything other than 0. He's never actually witnessed a machine breaking from measuring him and his abilities and their source is different from the usual abilities people get from magic crystals. The only thing he knows is that he's different but not in a way he can measure, prove, or show.