Why was the Initiative originally created?

The only ones who new exactly the old machines would come and destroy everything and everyone at the time the idea of the AI was created where the Geth. They also made the FTL-teleskope and somehow gave the data to the AI.
Thats why I´m convinced the Benefactor are Geth. And there are Geth on the Quarian Ark.

When you see those faces and hear those voices change, when Alex is speaking to the benefactor, that is one person who is using various faces and voices to disguise his/her face and voice. Garson was a front for the benefactor and even she didn't know who the benefactor was. 

I asked similar questions here: bsn.boards.net/thread/9894/story-andromeda-initiative

We didn't get far though...

Not bad.

I agree with your theory but this would be such a fundamental change in thinking for the Geth.  Seeing how we know that the entire Geth race didn't just suddenly disappear that would mean only some programs made it out of the MK which according to Legion would only weaken them and it isn't something they would do.  And to travel on the Quarian ark just seems to crazy seeing how most Quarian's either fear and/or hate the Geth although maybe that is the reason that ark has stopped or whatever it is doing.  Still I would welcome a Geth team mate as long as it wasn't Legion 2.0

They can travel dormant hidden in the memory banks of the arks. And something on the Quarian Ark woke them up, and the Quarians panicked.
And there is no reason for some distinctive 3th kind of Geth. It could just be a contingency plan from the non-Heretics.
I said already before the first official infos, while the speculations where running wild how the arks were build and funded that only the Geth would have the resources and "man"Power to build such a gigantic project in this short time, and stay hidden with it. Ok, Bioware decided otherwise, just some crazy people made all the arks in their backyard. But they got massive help from an unknown faction...

Since the Geth are software that do not require physical bodies to exist, they could find a way to install themselves into the Quarian ship's systems without the Quarians knowing about it. And they could have brought the designs for their physical platforms to be manufactured for them to download into when needed.

As for the rest, I don't know. I'm not really trying to make a case for the Geth being the Benefactor, that's the OP's idea. It is an interesting idea, but I tend to think the Geth are probably not the Benefactor. I am kind of thinking the Geth are involved with whatever emergency is happening with the Quarian ark, though.

And it would fit the theme of benevolent artificial intelligence in this game.

Geth make the most sense as they not only have the technology but the resources, knowledge and AI tech needed to build SAM. Especially the part of a symbiosis, thats what the geth do with the quarians if peace is made between them. The cooperative based AI is something extremely familiar to the geth. Finally we know geth have factions, the ones that joined Saren, the ones who wanted to make their own path so it will not be a surprise if another faction wanted to cooperate with the organics and move forward together.

The initiative is the third faction of Geth, the old machine worshipping guys got dealt with, while the ones who wanted to be left alone got wrecked when their Dyson sphere went kaboom via the quarians. Besides the previous games clearly show a theme that sure AI and organics might be different but they can work together for everyone's benefit.

Thats why if we get a quarian ark dlc, i will not be surprised if cooperative geth are part of the said ark and what the quarian warning was related too.

What if it was the Council? They knew the Reapers were coming but knew no one would believe them or everyone would freak the fuck out
so they sneaky funneled funds into the Andromeda Initiative in case they couldn't defeat the reapers so the council races would be able to make it to safety
That's why each race that was on the council had its own Ark while the others were just shoved into the Quarian ark (which, iirc, the quarians had to make themselves)and no other races were put in Cryo on the Nexus, even though the eternal space gypsies that are the Quarians would have been great at keeping systems running in case of the shit that happened in game.

this is a rich womans pet project that was taken over and turned into the largest refugee department in history with out anyone on it knowing they were refugees but the planners.