A time traveller warps into a plane that according to historical archives went down due to an electrical failure with everyone on board killed. The time traveller knows that the plane had plenty of empty seats so no one will notice that someone walking in the aisle wasn’t actually in the plane during takeoff. And of course he reasoned that since everyone will die he will not alter the timeline in any way.
He speaks to the passengers, finding out as much detail as possible about early 21st century humanity for which there is scant information following the damage caused by the techno wars. He stays for an hour and warps out minutes before the end.
The added weight of the traveller causes the plane to tilt ever so slightly – enough that the wing hits the water a couple of degrees lower than it did in the original timeline. At these speeds, even such a small change is enough to alter the fragmentation of the part, its pieces breaking off differently that they otherwise would.
Salvage boat 3 is tasked with retrieving the parts of the wing. The pieces have spread out in a pattern different than in the original timeline. The last piece is found about 5 meters further south than the location it wqs found in the original timeline, thus being retrieved 30 seconds later than it normally would.
The delay is enough to cause salvage boat crew member 1 to miss a green light on his way home. He arrives home a minute later. A cosmic ray streaming from the heavens towards the front door of his house does not plunge to the ground as it did in the original timeline but instead passes right through his genitals, killing off a sperm cell in the process. A sperm cell that would fertilise an egg from his wife during sex two hours after. The egg is fertilised by a different sperm cell. Only now the end result is an embryo with a different gender than what it would, changing the entire future line of descendants leading to our time traveller never being born.
You don’t have to kill your grandfather to generate a paradox. Anything would do it. And that’s why we don’t have time travellers saying hello.