This pretty much. The only reason for us to go to Andromeda is to avoid the endings of ME3 altogether and that is simply not possible if we leave after the events of ME3. But building the arks in secrecy is indeed possible and wouldn´t require that much of a retcon. During ME3 pretty much everyone knew about the project the alliance had going on, namely the crucible. Who is to say that this information wasn´t leaked by the alliance themselves to hide the construction of the arks?
Now you gonna ask, but how did they get the materials for the arks? Simple, materials were delivered to the crucible, we know that much. But do we know exactly how many were delivered? We don´t! That´s where one more retcon comes in. Materials intended for the crucible were rerouted to the arks, using alliance ships and personnel only. It´s quite easy to do so aswell. You simply calculate how much is needed for the crucible and the arks, and book them under crucible only. And with alliance ships fighting reapers everywhere, ships are constantly stocking up on supplies. So ships coming and going would be a common sight near the crucible.
Personnel? Same thing applies to personnel as with materials.
I'm sick of Bioware restoring to retcon's in order for the story to work, its a sign of bad writing. Also its made apparent that there is no plan B if the crucible failed since the galaxy is pretty much pouring all of its resources into its construction not to mention they can't afford the resources two extremely large scale project existing at the same time.
So why does Liara not know about it? She only shows us information that is imperative to our mission, namely defeating the reapers. But we also know that she has access to far more information than she let´s us see. Her hiding the information from us may just be a case of her not believing in the project in the first place.
That's just completely out of character for Liara not to mention yet another example of bad writing, she's not one to keep secretes from Shepard especially if its a matter of survival.
But that leaves one problem unadressed. The drives needed to get to andromeda, for which I have to admit, I have no explanation. Granted, you could use the schematics of the crucible and incorporate them into the engine design, but that still leaves the issue of having to discharge them.
FTL without the relay's is limited to short range at best, its why the whole idea of the galaxy suddenly developing FTL capable of traveling to other galaxies in the time frame of the trilogy is contrived.