You're writing such a post to an online forum, isn't that a clue?

What it's like to not exist for p-zombies.

Think: Deep Sleep

Is it possible to imagine oblivion? Imagine non-existence? — TiredThinker

Do you mean your own idea existence or everything? Only theoretically I imagine. And that’s still not the thing.

I mean having no sense of self and no perception of a world around oneself.

Is it possible to imagine it not being possible to imagine? Sure, as long as you're not pedantic and getting into pointless arguments about the meanings of the words you use to answer the question. You spent 13.8 billion years experiencing oblivion. You know what nothing is, and your inability to describe the experience of it is the perfect description of it.