I think "now" is an underrated concept in physics, as in a universal ordering of events, regardless of what order position and relative velocity cause them to be observed. If there is indeed a universal "now", then faster-than-light travel need not lead to time travel.
The light that we see today left them 10 billion years ago. Any light that leaves them now[1] will never reach us. And any light emitted by us now will never reach them.
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[1] Yes, I know, "now" is not really a useful concept when dealing with large velocities in Special Relativity. I don't think my overall point is destroyed by that, though. If you can find a more rigorous way to state what I am trying to say, please do.