[Hunpecked]

Suicide Junkie writes: "Even if you can't go FTL, you could still colonize the entire galaxy in less than 10 million years from here."

I remember seeing something like this in Carl Sagan's 1980 TV series "Cosmos", with a similar time scale. Presumably intergalactic distances are too great for "practical" STL travel (except perhaps by robots), but that just changes the problem from "first in the universe" to "first in the galaxy".

As for how we would detect advanced interstellar ships, presumably an expansionist species would colonize our solar system, or self-replicating robots would exploit it until all resources were consumed.

As for "them" detecting "us," I read somewhere that the Earth is one of the brightest radio sources in the sky. In Sagan's novel "Contact" the ETs respond to a TV broadcast of the 1936 Olympics.