Earlier quoted context omitted.
Even at (way) sub-light speeds, it's probably possible. Whether it's automated self-replicating ships (possibly carrying humans as gene sequences), or generation ships (seems pretty hellish!), a number of people have estimated mathematically that it's doable. Estimates vary wildly, of course, as there are many unknowns, but basically exponential growth gets unintuitively fast. Some links (there are many more pages to…
This is not "travelling" any more. This is sending spores hoping they will take root somewhere, but they will be forever disconnected from us, in space and, more importantly, in time . What's this mania you have of disseminating yourself? Even if you build ships that carry human genes sequences and send them on a million years trip, who is going to benefit? The sequences you sent?
I’m told there was a book on this exact topic. I’ve never read it, because other people tell me it’s now wildly out of date.