No start

Not a good thing. Sounds like it has slipped time as well as having a bad controller. The question now is, how far did it slip and did it do a lot of damage?

This might be helpful.
https://redlinespeedworx.com/2-0t-tsi-timing-chain-failure/

OK let's ignore the cams and go back to a "good" engine and start from scratch. I approached it as you had tested other items and had gotten to the code/timing as being the problem.

Run a compression test. It will tell you quick if the timing is off. If the compression is good then, Are you hearing the fuel pump prime? Run a pressure test and see what pressure the pump is putting out. Stick a spark tester on it and be sure it has spark.

OK, I'd probably wait until you get the adjuster. Install it, and see if it will start. If it doesn't then run a compression and leak down test. If you wanted you could get the timing procedure and reset it using the parts you have now. That would probably give you the best shot. Be sure if you do that, check the tensioner first. They do fail a lot. Not sure what you have for information but these would get you the same info that shops use. I prefer Mitchell but don't let that sway your decision.

http://www.eautorepair.net/app/YearsMakes.asp (Mitchell1)
http://alldatadiy.com/
https://www.chiltondiymanuals.com/

Yep. It has the complete procedure. It tells you a couple "special" tools are needed. Those are basically items to hold the chains in place as you work around them. You can use wire, tie wraps, string to do the same thing.

The tools just hold the chains as you work so you can get them into place without needing three hands. You'll see what I mean when you look at the book procedure.
It's like the special tool they have to hold the tensioner compressed for installation. The "correct" tool is nothing but a hardened pin with a rubber cap. Great if you're going to do hundreds of cars and don't want to have tool wear, but a common nail will do the job for a LOT less money.

So you put the chains in time but the engine won't turn over? Sounds like it is now either out of time or it did bend some valves.

Mitchell buries camshafts under Engine Mechanical -> Mechanical -> Cylinder Head _> removal. Then the engine code.

Which book exactly did you get, I'll see if the ones we access is different.
I know it's a 2012 VW Turbo 2.0 which I believe is engine code CCTA or CBFA. Which code are you using?

OK, the cams are out of time so the valves are hitting. What you need to do is look at the lobes on each cam, which ones are pushing valves down? Find those, then determine which piston is up and hitting the valves. Gently rotate the crank backwards to allow you to move the cam(s) until the timing marks are correct on the crank and cams. It may take moving each a few times to prevent issues OR you could unbolt the cam saddles and lift the cams, rotate the crank to the proper position, install the cams in the proper positions. Then deal with installing the chains. Which is the way I would do it. Faster, easier and less chance of damage.

I've used wire to hold the chains up, nail(s) for the tensioners, Zip ties and other items to hold parts when I run out of hands.