Impossible. One person can not, beyond any doubt, prove to another that he exists.
We can prove to ourselves that we exist (cogito, ergo sum; one of the smarter sentences uttered by a philosopher), but we can't prove it to others, just as they can't prove to us that they exist. We can only be certain of our own existance, and only at the present moment (future and past are just as likely to be illusions). That is all. Anyone who tells you otherwise is bullshitting you.
However, if we were to deal only with things we could be certain about, then we'd have very little to work with. So we operate with what seems most likely. But that's a different can of worms.
We can prove to ourselves that we exist (cogito, ergo sum; one of the smarter sentences uttered by a philosopher), but we can't prove it to others, just as they can't prove to us that they exist. We can only be certain of our own existance, and only at the present moment (future and past are just as likely to be illusions). That is all. Anyone who tells you otherwise is bullshitting you.
However, if we were to deal only with things we could be certain about, then we'd have very little to work with. So we operate with what seems most likely. But that's a different can of worms.