Imagine them departing when Shep was still dead or locked up by the Alliance between 2 & 3
Will you expand on this?
I think The Arks leave well before the fall of Thessia.
The Reaps are owning the Milky Way by the time Thessia gets destructed. Waiting on blue tentacle head stubbornness would get everyone killed
Some ARKs leave before Thessia... some ARKs leave after. That is what a "staggered" departure means. Each species decides for themselves when their ARKs leave... and the Asari leave it really late. Humans act quicker... using the info from their long-range scanners to get their ARKs on the way before the Reapers hit earth. They don't all have to travel right together... they eventually regroup in Andromeda... or perhaps part of the story lies in the various ARKs having to find each other.
I suspect that more ARKs were also still under construction when the Reapers hit... If you hatched a plan to build ARKs, it would make sense that you would keep building more and more of them until you ran out of resources or had enough to carry everyone (or as many as possible). Shepard says clearly "you know we're not ready if it is them, not by a long ways." (Perhaps meaning, we still have X ARKs under construction.) Later, Anderson can indicate (if paragon is chosen) that it's tough knowing "you can't save everyone." (Perhaps meaning, we didn't have enough ARKs finished to have even considered evacuating Earth entirely before this attack.)
Also, Anderson has been retrofitting the Normandy to use as a "mobile command center" - long before the Reapers attack. Question is - mobile command of what - an ARK armada? Where did all the resources Shepard had on board when he turned in the Normandy really go? Towards a Crucible that wasn't even known about yet... or an ARK project already well under construction?
The entire Refuge System and the Prothean Archives on Ilos we not accessible to anyone prior to ME1, but it was accessible after Shepard obtained the information on the "lost" Mu Relay. There was no logical reason for the Alliance to just stop investigating Ilos afterward... even if Vigil shut down as Anderson claimed.) When Liara is queried at the beginning of ME3 about why she's there, she says: "Process of elimination, mixed with a little desperation." That could mean that there were searches going on in other Prothean Archives. Those earlier searches might have yielded plans for the ARK project... but not plans for a weapon to fight the Reapers. So, while building ARKs, they continued to search for a weapon (a better plan), but were not successful until finding the Crucible plans on Mars. Having an ARK project secretly underway for as much as 3 years would make it easier for the Alliance to switch over ot building 1 Crucible after the attacks. Garrus says you go to war with the army you have... well, they could have departed with the ARKs they had ready and switched over to building a weapon they had just found the plans for to try to save the rest they had to leave behind.