Which part exactly are you seeking proof of, and to what standard?

"I know" is unprovable to others, unless you examine the wiring of my brain. (But then, what is "knowledge"?)

"at least one other human is conscious, otherwise the term would never have been invented." — it's always possible that I'm a Bolzmann brain and this was just luck.

I don't see how the term could have been invented by a mind that didn't actually have it, except with astronomical low probably random events.