WARNING: I AM A NERD
That is a self sustainment paradox. Since the timeline itself is not bound by the laws of time, any time travel you do would have been in the past to begin with. Theoretically, this means that a timeline would instantly change itself and adapt to a stable timeline or stable paradox if time travel is attempted. Therefore, our timeline is a stable timeline since adaptation is instantaneous. This means whatever time travel exists does not change the universe in any way, because the change had already been woven into the cosmic tapestry of the timeline. For example, if someone went back in time and gave someone else time travel, the timeline would exist in a way that before going to the past, the other person would have already had time travel, but the giver of time travel wouldn't have known, invoking the logic of shrodinger's cat: did they have time travel or not before humanity reached the moment the giver began traveling to the past?
However, that is only theoretical. In practice, you cannot affect your own life. If I went back to 1955 to stop something in 1985, both 1955 and 1985 already happened. Just because the moment I left the present did not happen doesn't mean that I was never in the past. Before I even thought of time travel, every adventure I had in the past already played out, as the past happened before I invented time travel. The past is set in stone. And so is the future. If I went to 2050 and became a music star and went back to the present, I couldn't stop myself from becoming a music star when I meet my younger self in 2050. Just because the natural progression of time hasn't yet reached 2050 doesn't mean I didn't skip ahead, then return to the present. Time itself is like a movie, it always plays at the same speed and cannot be paused or altered aside intervention of a higher being, such as the wielder of the remote. Time travel is like letting the movie characters use the fast forward and rewind buttons. Time is not relative to them, but to the natural flow of time. All of time exists as one collection of stories, like a DVD. We just put it in a player and are watching through it.
So, to answer your question, that is theoretically possible, but it's like putting an assembled model boat into a bottle. It's size is small enough for it to fit, it just doesn't have a way to get inside. It's possible to have a stable paradox, there's just no way to get yourself stuck in the loop in the first place.
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