I've suffered this before, but not on the TA (yet)
From a cold start it popped and missed and continued to run rough/rich.
Until...
I turned the engine off and restart and it ran ok.
Funny, as I seem to recall it started this around the same time of year as now.
Turned out to be the heater element part of the upstream O2 sensor.
Seems it wasn't heating fast enough, though the element wasn't broken.
As the cold engine warms, the fuel trim goes from:
Open Loop, a preset, start me up and warm me up quick, rich fueling set of values.
to
Closed Loop.
Closed Loop uses the up stream O2 to trim the fueling via heat in the exhaust, as the O2 self generates a small electrical charge depending on how hot the exhaust gases are.
So it Switches the fueling back and forth, from lean so the PCM adds more fuel, to rich so it takes fuel away.
This Switch in voltage (between 0.1v and 0.9 volt with the middle line being 0.45v which is perfect fueling) should take less than a second.
To do this quickly from cold start the O2 heats it's self rather than rely on the exhaust gas heating it (eventually) as old EFI did years ago.
A lazy heater element fails to respond quick enough, so when the PCM checks the Switch time in voltage from it against the Engine Coolant Temp Sensor and they do not fail within spec, the fueling trips into Open Loop System Fault and stays there.
So you drive around stuck in Open Loop System Fault which is rich like the Open Loop at cold start, but the exhaust gas have now heated the O2 and it will respond if required.
So now you clear it from the Open Loop System Fault by turning off the engine and restarting the car and Hey Presto, it runs fine again until the coolant and O2 sensor go stone cold again and you start all over again.
To go back to the System fault, it usually needed leaving overnight, but I did time it and got it to repeat after around 4 hours.
It drove me mad for weeks, as the Open Loop System Fault wasn't logged as a DTC, though could be viewed in real time when logging.
This lack of DTC I guessed was fact it only ever happened once every drive cycle (right at the start) and the heater element was complete (but slow) so didn't show as a open circuit fault..
The O2 (I thought) checked out ok, generating the right sort of signals when heated and the heater element resistance was reasonable when bench tested.
I even check the supply to the heater element from the fusebox to connector, all was ok.
By chance (rather than being clever) I pulled the down stream one which was same part, I also had a new one on the shelf.
When checking them on the bench, it became clear the original had a slight resistance difference within the heater element circuit.
To confirm, I tried all three in the Up Stream position.
The original failed again and again (a long process as the car needed all night to cool down) and the other two worked fine every time.