There are several ideas behind the nature of time travel, which are somewhat interesting to think about.
1) "Change the Past"
When you go back in time, it was not meant to happen. That means that anything you do could potentially change the future, even the smallest things.
This is the point of view where the paradox exists strongest.
2) "Everything was meant to happen."
This is the idea that everything that ever happens, including time travel, happens along one timeline. This means you don't just go back in time to kill your grandfather, you already have. Yet somehow you were born anyways, possibly you were adopted, or are an illegitimate child. This type of world the paradox is somewhat disproved by the idea that it cannot possibly happen, otherwise it already has.
3) "World Lines"
Everytime a choice is made, the universe splits into 2 or more "Lines". Chaos Theory supplies the idea that even if 2 circumstances are exactly the same, it's still possible for different outcomes to show. This means that there are many possible futures, all alongside each other. (Or alternately, many different Lines, all leading towards the same future."
In this theory the paradox is disproved because if you go back and initiate the paradox, it simply causes the world to shift to a line where you don't exist.
The other thing is what I noticed about materialization, since according to science it is generally impossible.
Especially related to Teleportation, there's usually 3ish different ways they go about how things rematerialize.
1) "Amalgamation"
When you materialize, your particles get mixed up with whatever particles are in the area where you appeared. If you missed and put yourself in a rock wall, you would be pretty dead. If you appear where another person was, you would sort of get mixed up together in a weird way. Usually the idea that air is there as well is ignored and nothing bad happens if you materialize in the air.
2) "Interception"
In the instant that an object materializes, it pushes any matter that was there out of the way.
For example, if a piece of paper materialized where a cup was, it would "Push" the cup apart, leading it into being cut in half.
If you materialized in a rock wall in this case, you would push the rock aside, but it will still probably crush you anyways.
3) "Replacement"
When you materialize, you replace all the matter where you end up. Either it just disappears, or it gets swapped to where you were originally.
In this case, if you ended up in a rock wall, you would stilll be alive, but you wouldn't be able to move ant would run out of air sooner or later.
