How did it get there? My theory is this: When you dropped the companion cube into the incinerator, instead of burning, it actually teleported 30 ft. from Breen, He saw it teleport and thought “Huh, what in the world was that?” He walked up to it and thought " Huh, this is cute ".
He then picked it up, and walked a couple of feet, when he tripped over a rock, and dropped the companion cube. The cube then started to transform, seeing as how it was NEVER supposed to touch Earth’s soil. It only took a day to transform into the citadel.
Well, that’s my theory :freeman: Discuss.