As I see it. Let's say that human civilization does not turn Earth to a nuclear wasteland but rather resolves its social issues and proceeds with colonization of Solar System. We already sent probe out of our Solar System. It does not look for me to be impossible technology to build a probe with AI and robots smart enough to reach another star system, decelerate there, build some factories on asteroids and copy itself sending copies to further star systems. Of course at the same time exploring its "home" star system and transmit information they got to Earth.
So very quickly (in universe scale) our sphere of knowledge will expand limited only by some fuel tanks capacity required to accelerate and decelerate.
Yes, there will be years, decades, centuries and millenniums for this information to reach Earth. That's the nature of cosmos (according to our current knowledge) and we will have to deal with it.
Eventually probe will find planet with life. May be life is more abundant than we imagine now. May be not. Surely there will be protocols for the probe to investigate life. It's hard to imagine what those protocols would be. May be explore freely until certain technology advances are observed and then hide. So may be our ancestors saw alien probes on a regular basis and just didn't care. But now those probes observe that we've got quick airplanes so they hide better.
My point is that developed civilization inevitably will expand its sphere of influence at speed limited by speed of light. Probably slower than that. But billion of years at 0.1c is still huge chunk of universe. Are we sure that no civilization born within this radius billion years ago?