Yours is a common theme of science fiction time travel- change the past and do you muck everything up or make it better? If someone kills Adolf Hitler's father before he meets Adolf Hitler's mother, then what?
Some believe that things even out. There was a Japanese factor to World War 2 and perhaps Germany would have found it's way to the axis side no matter whether Hitler took them there or not.
Perhaps, if you didn't answer that door that day, you would have been found another day.
Others (myself included) subscribe to radically different outcomes were it possible to change things. Although it is just philosophy and not mathematics, many serious scientists suggest that traveling back in time would not allow any change. They state that were someone to interfere with the past, then in all possibilities, they ALWAYS DID INTERFERE WITH THE PAST and nothing ever changed. They believe that any ability to tinker with time would eventually have been discovered and all of time would be unstable because of it and it would unravel to the point where none of our universe could exist anymore.
I know that's not really where you are going. But I feel it is important to consider that "What if...." is not really something we can dwell on for any serious progress. It is just a curiosity and nothing more.