That's my thought as well. Last time I was put under anesthesia I tried hard to think about how I was feeling. I went from awake with my eyes open to opening my eyes. I thought my eyes were already open? There is just literally nothing between that span of time.
It's like that except you don't wake? But it lasted an instant. How can something that passes in an instant last for infinity? It makes my brain hurt.
Indeed it does. This is why I try to remind myself that this kind of thinking can only torment me when I'm alive, and I should stop wasting time. Especially at 2am, which of course is when I have these kinds of thoughts to begin with.
My dad and I used to talk about this and decided that we lived forever, as a practical matter. "Before" and "after" just speculation.
The closest survivable analog, in my opinion, is the "sleep" you experience when under something like sodium thiopental. When it works, you go from awake to awake again in an instant, from your own perspective. A bit jarring to lose hours or days like that. I assume death is similar but without the waking up part.
Regular old sleep doesn't involve that level of unconsciousness.