Eight billion years, perhaps half or more of a star systems allotted time.
Our Sun is considered to be at least a third generation star (based on content of heavy metals), which means at least three other Earth evolution cycles could have occurred already since the Big Bang.
We know that life on our planet began very quickly. In geologic terms, almost as soon as the rocks had cooled. Maybe this is a unique event, or maybe not, but if we assume not...
Then granted that it took 3.5 billion years for self awreness to arrive, but the universe is 13.7 billion years old, and the distance between galaxies may be uncrossable, but the time it takes to colonize a standard galaxy with a diameter of 100kLy is much less than a billion years, even crawling along with the technology we have today.
So, even a single successful civilization out of the billions of stars in every galaxy *should* be capable of colonizing the whole galaxy well within the lifespan of its progenitor planet (assuming of course that our situation is not unique).
So Yes, we are *already* here. And more importantly, our galaxy and all others should be swarming with Von Neumann machines at least three times over since the Big Bang, and yet, they are not. This is the Fermi Paradox, and it's a good one. Either the conditions we have as examples are unique (though increasing evidence shows more and more environments which are similar to proto Earth), or we're missing something fundamental in our understanding of what limits life in the Universe. Or, the Universe is full of intelligent communicative life, and we just don't recognize it for some reason.
PS, the links in my previous post lead to more detailed information on the Fermi Paradox, and to Von Neumann machines.