[S4M]

If you want to speculate, how about the possibility of uploading people's mind to a robot? Let's say that we are able to send outer space a bunch of self replicating robots (they can travel to various planets and build a copy of themselves using the raw materials they can find there). After some time, we have lots of robots at many points in space, then you make a copy of your mind and send it at the speed of light to those robots. Because of the self replicating nature of the thing, we can have lots of robots so anybody who wants to can upload his/her mind to one of them. That way we have a non risky an relatively cheap way to explore the galaxy - it would just take couple of thousands of years to have everything set up.

[XorNot]

Still a relatively slow way to get around. We have some co-factor here for "median time between alien contacts" which might be thousands of years. In which case they came, they saw, and the people who saw them remembered it as folk tales.

[scrumper]

"Speed" could be seen in terms of perceived time for distance covered. No reason with a robot-uploaded consciousness that you couldn't slow its perception of time such that travel between the stars becomes something comprehensible by a human-like mind. A bit like video game time acceleration, but real.

That doesn't address what happens to the visitees, but if that kind of slow-scale exploration becomes the default, then any civilizations on a similar level to the robot explorers would have technology and societal structures in place to support meaningful contact of that nature.