My S3 did this, it was the crank angle sensor, in the block down behind the filter housing where the gearbox bolts on. Easily the most likely failure that shuts down the whole engine. I can't recall if that shows up in the ECU as a fault. It certainly does in the ME7 ECU but yours is an ME3.8
Coilpacks on the Golf are pretty good but the ignition amp, in the back of the airbox, normally only drops one cylinder at a time if it goes.
First step is to scan it with VCDS.
Gavin
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