Ok, this may be a brainlet question, but it seems to follow logic to me and and I'd like an answer.

When we see stars in the sky, we see them as they were in the past. Because it takes x amount of time for the light from that star/galaxy/whatever to reach the earth.

So, does that mean that if I happen to be looking at the right patch of dark night sky, at the exact right moment when the light from some new celestial body reaches earth for the first time - from my point of view would I just see a star appear out of nowhere suddenly into the sky? Like it just blinked into existence?

If this is a thing, is there a name for it?