"Future cannot be changed, but the past can, as long as it leads to the same conclusion."
The moment of start of the travel is a fixed point. But the past wasn't at all how you remembered it.
What can change is the knowledge of the time travellers, and events can be put in motion, that will not bear fruit at the moment of start of the travel, but will extend past it in a way that would not have occurred had the time travel not happened.
The movie "Primer" had something along these lines:
One of the protagonists knocks out his past self and stashes "himself"
in the attic, then proceeds to go through the day, planting ideas in
others' heads, subtly affecting the world, following the "rails" into
which the universe ! forces him and when the natural time flow
catches up with the hour he had departed, at the end of the "trip" the
world appears just the same as when he had departed, but the events
that he knows had occurred are not at all as he had remembered them
from the first time around.
The time traveller is bound by invisible "rails of fate", physically unable to stray far from them; but there are freedoms he can take, do things in different ways; often significantly different, which will lead to that one fixed point in time to be "as remembered" but the results vastly different.
Say, in the future the authorities discover a nuclear bomb planted in the middle of the city. Disarming it is very difficult, probably the effort would fail. They find traces of the bomber, a notable terrorist who had arrived at the city two days ago.
You travel two days back into the past. You can't just kill the terrorist and deliver the bomb to the authorities, changing the future. But you can knock the terrorist out, sabotage the bomb, then plant it yourself along with evidence that it was the terrorist, and when the countdown ends, the bomb won't explode.
(you may resist the "rails of fate" and can change the future, but it would be a very unpleasant experience, literally pushing against moving walls that try to guide you like a puppet.)