kent davidge said:
Even if we manage to travel back in time, according to relativity, we could never travel to a moment before we started our journey, right?
As you state it, this makes no sense, since "travel back in time"
means going back to "a moment before we started our journey".
I think you need to rethink your question.
You might possibly be thinking of statements regarding using wormholes as time machines, in papers published by Thorne and others in the late 1980s, along the lines of: you cannot use a wormhole time machine to travel back to any time before the wormhole first became a time machine. That is true (for the class of wormhole time machines being considered in those papers), but it doesn't mean the same thing as what you say in your question. (See further comments below.)
kent davidge said:
I could not enjoy some moments again with a relative that passed away, say 10 years ago?
You could if you were living in a spacetime that contained the appropriate timelike curves. For example, if there was a wormhole time machine that became a time machine prior to 10 years ago.
Note, however, that if you were living in such a spacetime, the events of you enjoying those moments with your relative would
already have happened 10 years ago. In traveling back in time, you would not be "changing" things so that those events happened where they otherwise would not have happened. You would simply be participating in events that are part of a 4-dimensional spacetime that contains wormhole time machines. For more about this, look up the Novikov self-consistency principle.