Here's my theory to go with the dozens that have been concocted:
Hackett always believed Shepard, all the way back to Mass Effect 1. Once Sovereign manifested, he knew it was only a matter of time before there was some kind of life and death battle for survival, so he initiated the Alliance construction of the Ark ships. The scenes in the trailer with Earth as the background (I do believe it was Earth) show the Arks complete or near-complete. This dates from during the time Shepard was incarcerated for six months after the events of ME2 Arrival DLC. It's possible that Shepard was consulted on the framework of the Ark mission. When warnings of imminent Reaper arrival started to appear (Anderson's line at the start of ME3 "Something big's headed our way") that was the cue to release / launch the Arks. And not a moment too soon, since the Reapers arrived shortly after.
(Not sure about the Shepard send-off from the N7-day trailer. It's possible the Arks were launched because of an imminent Reaper threat, but if Shepard did the send-off, (s)he would almost certainly have been apprised of the threat, making his conversation with Anderson at the start of ME3 redundant.)
The largest problem with this that I can see is that even if Hackett starts building the Ark ships after confirmation of Sovereign's existence (which, if Shepard's video link and comms were being recorded, was Virmire), that's still an incredibly short time frame for building three ships the size of these Arks - THEN setting out to build the Crucible (material shortage anyone?). There's also the fact that there was zero hard evidence of a Reaper invasion prior to it actually happening, so Hackett & the Alliance would have had to invest a ton of resources, time and effort into something that was, for all they knew, pointless. Unless the way that the project was funded was as a deep-space exploration project - viable because of, I don't know, environmental concerns in our current galaxy? (Dark energy concerns return! lol)
...I think I need some of ZipZap's Ryncol...