There are levels of intuition: from the reasoned guess, to the vague hunch, to the crystalline insight.
At the level of the crystalline insight, I know for certain. Now.
I'm not at all certain if this life on earth is anything other than a matrix-like subjective existence, however, but that is another (related) question.
You might call it an unshakeable belief, but using the word belief already takes it far away from what it is. Any ordinary intelligent person can develop themselves to the point where this will become crystal clear to them, but no amount of argument from others will short-cut that process. Believe me (!) if I could gift it to you, I would. It would save me from endless numbers of frustrating conversations. I attend a discussion/dialogue group, and some of them are forever trying to get me to accept that this is just a belief, and it isn't. (except for one other member who is on the same page, who just smiles ruefully and shakes his head that I have allowed myself to argue the toss with them yet again)