You are the end result of a “would you push the button” prompt where the prompt was “you have unlimited godlike powers but you appear to all and sundry to be an impetuous child” – Zero, 2022
There is no time machine. It's done through magic. :|
I mean if you're going to have a method of travel that leaves no discernible evidence, and goes forward in time to a a period where anything you could've taken with you is materially still available, you don't have many options in the way of proof.
Maybe carbon date a first-publication of the first Harry Potter book or something.
Connect yourself to a missing-person case from the date of your disappearance, have sufficient identification on you to start an investigation, and try and get some sort of dental record confirmation.
Alternately if you're trying to keep it quiet, find a loved one who's still alive and tell them something only you would know.
If you're planning to return to the 90s and the universe is Novikov-self-consistent, have someone give you a sealed envelope, then go dig up that envelope somewhere where it only could have been buried in the 90s or earlier and open it, then make sure to go back to the 90s and bury the still-unopened envelope there. Technically this only proves that you're going to go back to the 90s at some point, not that you're from the 90s, but I think it should suffice.
Comments
...wait
Or bring an old computer or SNES that doesn't have yellowed plastic.