I'd've said that myself up until yesterday. I was pretty sure that the mission to Andromeda would be a contingency plan to escape the reapers, but given the fact that you seem in the trailer to be leaving from pre-invasion Earth, and the amount of resources that would need to be put into the building of a ship on such a scale, it seems unlikely that it was built concurrently with the crucible. For now we still don't have nearly enough to go on to jump to any firm conclusions. We'll just have to see what explanation they give us...
I wouldn't take the trailer that literally, departing earth is more meaningful with all the actual astronaut footage they cut in.
Even if it is pre-invasion, its possible the project started three years ago after Sovereign's attack, which is a slightly more believable time scale.
And we still don't really know what the scale is. It looks big, but that's a wide window. A Reaper is two kilometers long. The Citadel is 44.7km long. Of the two, I'm guessing its closer to Reaper size.