In Ray Bradbury’s A Sound of Thunder, Eckels hires Time Safari, Inc., to take him back to the Late Cretaceous to hunt a Tyrannosaurus Rex. When he faces his quarry, he loses all bravado and panics. He leaves the path, steps on a butterfly, and alters the present-day. Words are spelled differently. The other candidate won the election.
McCoy steps through the Guardian of Forever and stops Edith Keeler from being hit by a car. Keeler delays the US’s entry into World War II, Germany wins, and the Federation ceases to exist mid-sentence.
Marty McFly saves his father from getting hit by a car (different car) and almost erases himself from existence. Barry Allen saves his mother from getting killed when he was a child and… you get the picture.
It’s a trope of science fiction. Time travelers are always concerned about changing the present by making some small change in the past, but we never think that we can seriously change the future by making some small change today.