Under that first scenario, then, the way out of the paradox is to note that whatever it is that you would do and affect by traveling back in time has already occurred. The way the Universe arrived at its present state is due, in part, to the actions you took at every step of your existence, including the steps where you traveled back in time.
The thing you give up, though, is the ability to change the Universe through your own actions. You’re well aware that, today, the actions you take have incredible importance for tomorrow’s outcomes. Whether you go to work, punch your boss, or drive your car into the sea have tremendous consequences. But if you traveled back to the past and acted there, those consequences would already have been determined. It’s an unsettling thought.
The second way out is to assume that the past isn’t written, and your actions do matter. The Universe, as it exists today, is not bound to the state its in right now if you travel back to the past. In a way, every action you take creates a new, alternate history for the Universe. You can kill your own grandpa before your parents are conceived; you can prevent your parents from meeting and falling in love; you can kill Hitler before World War II or assassinate Brutus and Cassius and Marc Antony before they assassinate Caesar.
In short, you can change history.