OK, so for the longest time I thought that my '09 Audi A3's 2.0 TFSI DSG S-tronic 6-speed was stuttering from a complete stop because that's how those transmissions drove. When we took it to the dealer while still under warranty, that's what they said too. I kinda gave up after numerous attempted fixes myself.
Fast forward to my new-to-me 2013 Audi A3 2.0 TDI DSG 6-speed transmission, and the difference is NIGHT AND DAY! I have also test driven a 2011 A3 TDI and also a 2018 A3 TFSI recently. They all use the same DSG 6-speed transmisison, but the driveability is completely different.
The 2011 TDI stuttered a bit, but much smoother than the 2009 2.0 TFSI. Still not quite smooth like a torque converter transmission. The 2013 TDI felt almost exactly like the 2018 TFSI. They both engage the first gear much faster and smoothly, which makes stop-and-go driving far less frustrating than the 2009 TFSI that stuttered like the engine was going to stall going from 0 to 1st. The 2011 and 2013 TDI had DSG firmware updated for the diesel emissions fix, the 2018 was stock.
So my conclusion is either 1) the software has been vastly improved for driveability, or 2) the mechatronics in earlier iterations really sucked. If your DSG sucks, I strongly suggest you find a way to convince your Audi dealer to check and update the mechatronic firmware. It's worth a try.