The scenario of someone going back in time and changing something in their time line and then returning to their time line is not possible.
If time travel is to ever be possible, there must first be a way to identify every possible time line that exists (which would be infinite).
If you had no way to identify which time line to time travel to, there is no way of knowing where you would end up and no way to get back to the same time line you just left.
Time travel would require that we have some way to identify not just a time and place in time but also a time line, time, and place in time. Infinite time lines would require that there must be some identifying marker which exist in every time line with which to identify individual time lines if time travel is to be possible. A Time Line DNA of sorts. Something specific to each time line and only that time line. Something that is not associated with current events or people in existence. Something more prevalent throughout the universe because time is not caged in to just our reality. Our time line exists to the ends of the endless universe and any change would be seen to the very outer ends of our time line in our endless universe. This marker must be something that intertwines itself into the very fabric of existence on such a micro (or beyond) scale that it can not be seen or understood by us at this time. Somewhat like DNA is to all living things. There was a time when we did not know DNA existed. This could be similar. A marker that identifies every reality and dictates its makeup.
If the existence of such a marker could be proven, then the search for time travel could be accepted as viable.
Although, I believe that it would be easier to switch time lines and pick one that had the variables you wanted rather than going back in time and trying to change something to change the current reality. So, the only practical application of Time Travel would be for observation purposes only. Because any possible change that you could make will have already been made in another time line and it would not be new. The time line you would be trying to create would already exist and you would not change the time line that you were in. In effect, all that would happen is that you would change time lines. The old time line would still be there.
Also, I believe that it could be possible that when you have Deja Vu, you may have just traveled through or may be remembering one of the other infinite time lines for a brief moment.
Have you ever noticed that sometimes when you have Deja Vu that you remember more than others and sometimes just few things are the same and at other times a lot of the things are the same. If there are infinite time lines, it could help to explain this phenomenon.
Ponderous isn’t it?