Branching makes it difficult.
Thing is: if you believe that there’s no free will and that physics handles it all already and that randomness is also simply difficult structures but ultimately calculable, then you probably don’t believe in branching but in a calculable universe.
If the universe is wholly calculable and no information is lost , then there is nothing to prevent time travel to the past, as you’ll have a block universe notion.
BUT, if you accept branching, time travel to the past may still be possible but extraordinarily difficult.
BUT if you think information does get lost, then you’ll conclude that time travel to the past is not possible.
I personally don’t — and never have — found the “Oh No A Paradox” a convincing argument AGAINST time travel to the past.So what if it’s a paradox? Lots of stuff are.
In my random spew of thoughts, I’m of the “branching makes it difficult” opinion. So, maybe so.
At the very least, you should be able to travel back in time to the moment you had a working time machine.