If you want to prove it to yourself: just think. Only existing things think.
If you want to prove your existence to someone else: post something. Only existing things can write posts.
If you want to prove your existence beyond some realm similar to the simulation hypothesis to someone else, then you can't. Anything you do could be simulated.
The first one still applies in the simulation hypothesis though, so at least there's that
>also: >>>/lit/