I don't know if that would be the outcome, because of those that are convinced of your existence, that isn't necessarily how they act.

Now back to the first part, would you prove yourself? I don't know how you could prove yourself to all people. Not everyone believes in gravity, a round world, evolution or climate change even though I may say there is enough evidence to support each theory. I don't know what act would be proof-ful enough for every person. And if we say that rather than an act (that people can assess) you just whisper in every person's ear, and then they know you are true, then this isn't really proof, as it could also be seen as mass psychosis.