Well, to be fair, he only has to hit _that_ goal - at which point he can go back in time at his leisure and fix all the others. And he could hit even the time machine goal as late as he wants, and it won't matter.
Something something 'light cone.' If the machine was turned on a million years ago in another star system and then brought to Earth, the Primer model would put you in the other star system when you climb out of the machine. And then you'd need to make your way back to Earth. (It's unclear to me whether you would continue aging while sitting in the box and waiting for a million years to go by in reverse... But I assume you would.)
So I think the 'other civilization' thing only works if they're already approximately here with a running machine.
I think we can tell for certain that time travel will never be invented because if it were to happen, then logically we’d already be experiencing people visiting us from the future.
Elon in 2026: “by 2028 we’ll have FTL drives”
Elon in 2028: “time machine!”