In many books/comics/movies/etc containing time travel, characters are very cautious about causing a time paradox (like a grandfather paradox). Most of the time, it ends up just fine. For example, in Back to the future, Marty prevents his parents meeting, but the plot-induced rules of time travel make his brother and sister disappear first (over about a week), and even himself disappears very slowly, giving him time to fix things.
I remember reading some time ago (a few years, but the story could be older) a short story where the exact same warnings are given about paradoxes, and as in most stories, the main character doesn't really take it seriously, but there is no plot-armor this time, and he literally creates a grandfather paradox and destroys the universe.
If it helps, I'm sure I read this story somewhere online, even though it probably exists in a book somewhere too. The story was a short read, but at least a few pages.
I remember reading it while doing something else and really not paying that much attention so I barely even remember any details except for those. That is why i'd like to read it again.
It is not the story with a brick that a scientist decides to not send back in time after already receiving it in the past ("Experiment" by Fredric Brown), even though I guess the premise is very similar.
Edit: I'm pretty sure the main character was either a male teenager or Young adult male, or at least there was one accompanying the main character during the story.
I also think I remember that they didn't go that far in the past, I'd say less than a hundred years, and they met at least one relative/ancestor who didn't recognize them at first.