So, why no one ever mentioned the Andromeda Initiative in the trilogy?

Why would they mention it? Why do they have to?

We saw things through the eyes of an Alliance officer and we (Shepard) didn't even know where/how the citadel shit was being built or which corporations were involved...
We knew and had access to the military focused data and information we needed to complete our mission... plenty of shit going on in the Galaxy including huge Corporation projects that didn't make it onto Galactic news networks

It being a retcon is the obvious reason.

If you want to try to write in a reason, Shep probably never heard about it because as far as we know it left during the time when they either thought Shep was dead or working for Cerberus, so the Alliance wasn't exactly keeping you in the loop as to what was going on in the galaxy.

By the time ME3 rolled around it was already gone, and wasn't going to be of use against the Reapers.

We don't mention CERN in every day conversation.  Nor the Lunar Landings nor most things that happen in human history really.  

The crew in ME1 would have all been deployed somewhere else and wouldn't know the details of the AI.  That's assuming there isn't one parked above earth. 

Not to mention, everything in the AI seems to be cutting edge technology. The Normandy that was an exceptional ship for the Alliance is nothing compared to what the AI is building. 

And there are plenty of contexts where it would not be neccessary.  Besides we do not really know how much of a common knowledge the AI was during the events of Mass Effect.  Or even if people thought it would even work.  We have no context when you get down to it. 
We do not know how the Arks even work though enough to know whether the technology could be adapted for military use.  They could have been essentially pointed in the direction of the Andromeda Galaxy and fired at it at extremly high velocity.  We just do not have enough information yet. 

We don't know the method used.  For all we know in order to bypass the discharge problem the ship has to be roughly the size of the citadel. 

Because Andromeda is part-prequel and ya know, that's the issue you always get with prequels

Why do I feel like Arcian and SofNascimento are not going take any other answer other than Bioware sucks.

It is quite obvious it's a retcon. But at this point if Bioware wants to respect players decisions in ME3 and avoid the adressing the catastrophe that is ME3's ending they are going to have retcon. Frankly I don't really care. None of the info they have given us is offensively lore-breaking. I'm sure they will provide us with some sort of excuse for why nobody mentioned it but that doesn't really matter that much in the grand scheme and it won't ruin the game. The only thing I care about here is that I get more Mass Effect.

Better yet, where the hell did they find the resources to build a warship the size of the Citadel?

In ME3 we had to get most of the races, and a shit-ton of resources, to build the crucible. When, and how, did they do that? In their spare time? :/