I never had any noise leading up to the malfunction of the Tranny. I still have the noise.. Friend suggested I may have popped the belts in one or more tires. Plan on replacing all 4 tires in the next week or so and see if it goes away...

 

I have precisely the same problem and my car is now in the shop for a complete transmission replacement under warranty (my car is a little over 2 1/2 years, 2015, but is very low mileage). My experience was virtually identical in the way it happened, progressed and the brief recovery by turning the car off/on. Car went in Monday and I was advised that afternoon with an almost identical description of what went wrong. I am supposed to have it back by no later than Friday.

 

I gave up on my A3... recently traded in for '17 A5 and couldn't be happier.
The noise in the cabin was caused by cupping, which according to the dealership, was caused by not having AO tires. Thats right...my dealer tried to tell me that tire cupping was caused by not having Audi Original Equipment tires. Needless to say, i won't be visiting this dealership anymore except for the free car washes...

 

To be honest, I am otherwise pretty happy with mine, but I think Audi is having some problems with the consistency in quality with manufacturing them outside Germany (which presumably keeps the price down). While the car still has many Audi marks of quality, it shares more in common with VW's than any previous Audi I have owned (all A4's).

As far as noise goes, I have not had any problems (my brother has a BMW 3 series and comments how much quieter the A3 is), but I am driving a 2016 A3 loaner while mine is being repaired and it is substantially noisier. There is a vibration/hum/resonance that does correlate with speed. It can't have anything to do with non-OE tires obviously, however, it might be related to alignment or something like that--I noticed definite scraps on the rims from curb impact (although in my experience Audi's do not easily go out of alignment from that). In any event, if someone asked me about buying one, based on my car, I would point out a couple of things and recommend it. But based on the loaner, I would say you have to take a serious test drive first.

 

Same thing happened to me with my 2015 Audi A3, took it to the dealership in Concord California, and they just confirmed I need a new transmission. This vehicle only has 100K miles and all services done by AUDI.
This is a ridiculous and AUDI should put a recall on this transmission issues instead of wanting the customer to pay $12k for a transmission replacement.
Totally irresponsible from AUDI to think customers should deal with the repair cost when this should abiously labeled as an "UNSAFE RECALL".

 

This is almost exactly what happened to me, though mine died faster. One second I was fine, a minute later only first gear. I was able to limp into the dealership, a 25-minute trip that took nearly an hour. Total transmission replacement. Fortunately for me, I was under warranty.

I did end up getting another A3, 2018 model year and have had no serious problems, the only issue was I was told an alignment was needed. In almost 20 years of owning Audi's I have never needed one before. I probably should have challenged the diagnosis, but the dealer has been very good in the past.