So, typically the wideband's signal isn't used until the sensor is fulled heated, which takes about 20 seconds or so. This means that a full cold start with no sensor, the car will run without o2 sensor data every time.
So you can unplug the wideband controller from the ecu and see if it makes a difference. If it improves, then something is likely faulty. That's extremely unlikely with a wideband though, since the controller outputs the signal, not the sensor, to the ECU. If the controller fails, it typically reports nothing to the ECU.
It's more likely the MAF.