Its an interesting thought experiment. I think, time travel is likely impossible because it would likely violate obvious laws such as conservation of matter energy ...
There are no laws. You are using this in the fallacy I call the Argumentum ad Legem = laying down the law. There are observed functions in the universe. Conservation of matter and energy is how the universe appears to work. Scientists made a neat formulation of this. In science a handy formulation of a theory is called a "law".
As the bumper sticker says, "186,326 miles/sec. It's not only a good idea, it's the Law."
Now, time travel is teleportation. Let's examine the effects of teleportation. I'll teleport like a movie special effect to a spot in the parking lot outside and come back in.
Ow! OMG, that hurt. I teleported to a place where there were oxygen and nitrogen molecules already in the volume I took. They incorporated into the molecules of my body. I think I killed a few cells including some nerve cells. I feel sick. Atoms themselves overlapped creating tiny explosions as they separated. At least I projected to a point an inch above the pavement. Incorporating shoe soles into the pavement wouldn't have locked them as some superdense matrix. They would have gone off like a bomb.
Let me try again. I can fix this.
Much better. Other than the pain in the ears. I'm a little deaf now -- dang -- blood. I broke an eardrum. This time I used a teleporter that has a complete mass exchange -- some consequence of thermodynamics to be figured out later.
This machine did a complete exchange of matter. I weigh 80 kg. Air weighs 1.25 kg per cubic meter. So it had to suck out a volume equal to a 4 meter cube. Think of a 13'x13' bedroom with a ceiling 13' high. The momentary vacuum was refilled by ambient pressure the way it rushes in after lightning passes. I was at the center of a thunderclap. And back in my apartment the windows were blown out.
Like the time traveller in the cartoon above, these things conveniently don't happen. Note that Daniel Jackson had to speak Russian to Russians. I came in late to the show and thought the premise was like the movie, and that Jack O'Neill and Capt. Carter had had several years to learn to speak the galactic language which was a dialect of ancient Egyptian. Instead not only our galaxy speaks American/Canadian English but so do the Wraiths of the Pegasus Galaxy.
Terra Nova (I missed the premiere) at least makes sense that every trip back in time splits off a new time line. So the people of Earth can recolonize Earth over and over starting with splitting off the Cretaceous Period 20 million years before the Deccan Steps and the Chicxulub Meteor wreck everything.