>If you could travel back to a previous state of the universe, you would change the state

It depends on what's happening with that 'travel'. Are you rearranging the present to resemble a state it was in in the past? Or Actually going back in time' as shown in scifi films? In that case, you wouldn't be able to because as soon as you did, you'd never exist as you are in order to go back in time.

Unless it causes branching which avoids this. I wonder if you could ever travel back to the exact moment and branch that you came from?

When travelling back in time, you wouldn't be on Earth any more since Earth would have been in a different position back then. So you'd find yourself where Earth was 50 years ago (if you go back that far), looking at our solar system from a great distance.

Perhaps there are many frozen time travellers in our wake. You'd need to work out exactly where our solar system was during the time you wanted to travel back to, travel there first, and then travel back in time. Or the other way around.