Why are Kett and Angara languages translated so soon?

Because of ME:A's cheap knock-off version of Halo's Cortana, aka SAM.

There are a lot of things in MEA that can be called "space magic" but breaking the language barrier, IMHO, is not such a case. There are enough hints in the game to create a full and logical picture of how and when Ryder starts understanding both Kett and Angara. I wanted to write this for a while, so excuse the wall of text.

It has been some time since I played the game, so feel free to correct me if I am wrong about something.
At first we arrive at Habitat 7. We don't have a clue about what the Kett are saying. Then we hit Eos and come across several datapads that contain Kett recordings. The only word that I recall we understood was "Salarian". This doesn't mean it was translated since the Kett probably just pronounced the name of the species. Next stop - the Kett ambush in space where we meet the Archon. Now, remember that the Kett actually know every Milky way language by that point. They had the Salarian ark for a while now, interrogated prisoners and had access to all the information contained on the ark about the Milky way, including languages. During the ambush we didn't translate the Kett language. The Archon chose to speak to us in English since he obviously wants to make contact - Ryder became important to the Archon after the activation of the first vaults on Habitat 7 and Eos. Important enough to be spoken to during capture. It is not explained if the Archon speaks in English or his translator transmits to us in English, but it doesn't really matter. At this point we still don't have a clue about the Kett language, but the Kett can communicate with us if they wish.

Next stop - Aya. During approach we are intercepted by Angaran ships. We don't understand a single word they say, but the Angara understand us perfectly. It makes sense since they had contact with the Exiles on Kadara and even used human agents (Reyes anyone). The Angara have knowledge of our language which is obvious during the dialogue before landing. If Ryder makes a joke, the Angara on the comm laughs before we are escorted to land. If Ryder doesn't choose the joke dialogue option, the Angara doesn't laugh. Obviously the Angara didn't want initially to give away the fact they understand us. After we land on Aya, it is the Angara that choose to speak to us in our language. At this point we still didn't decrypt or translate crap and have no clue about the Angara language.

It is not stated in the game in any way that I recall, but I believe that after the events on Aya, the Angara give us everything we need to understand both Kett and Angara languages. The Angara obviously know the Kett language after decades of contact and war. And now we are sort of wary allies with the Angara. We are given missions to operate in Angara space with Angara operatives against the Kett. It is not hard to assume that the Angara will share with us their knowledge of languages since it is vital in this joint venture.

If you go back to Eos after Aya and activate the same datapads that were in Kett language, you will find they are now in English. So yeah, I don't think SAM decrypted anything, it's the Angara that gave Ryder the knowledge to communicate.

So we can get the fuck on with the story.

Err... I was not joking, SAM is a cheap knock-off of Cortana. And a very poor one at that.

Whatever you say dude.

Dude, I think it's time for you to lay off the cheese, man. Because I don't use a pc.

When I said cheese I meant cheesing.

You can't eat cheese?  It's one of the best things to ever happen to food.  And if you hate W10 so much use 7.  I don't see why you would, as 10 is faster and more secure in every single way.

You cannot delete Cortana. Microsoft embedded Cortana functions in many basic operating system files and then made them all depend on the Cortana executable to work. Windows 10 *will not work* without Cortana present.

Cortana can be set so that it's entirely in the background, deaf and dumb, unable to do anything.

Windows Store executables are also required for several useful programs, like the built-in Calculator. Without the Windows Store, Calculator will not work. Unless you install an older one from Windows 7 and make it the default.

That's pretty much how I understood it. On Aya, the angara seem able to understand Ryder immediately even if they don't let Ryder in on that and with that, it seems like Ryder's ability to understand them in the initial meeting is because of the angaran's translators and not because of Ryder's.  

It's likely the same with the kett who also encountered exiles and who we know, based on audio recordings, captured colonists to gather information about their biology. 

No, it's not. The problem is that Cortana has permanent and irrevocable access to microphone / camera and has system privileges. From a network security standpoint, it is a mistake of massive proportions that should never have been effectively part of the core OS.