If it's happening that fast, it's likely a blockage somewhere. Chances are it's in the coolant return hose that goes to the overflow bottle. They're prone for blockage, and will immediately cause pressure to build up in the system.
If you have a turbo diesel with the split main hose that goes over the alternator, and it has a seam 'welded' overflow hose coming off of it, it may have a restrictor in it near the overflow bottle. You'll see a bulge in the hose near that end. I'm not sure why VW did this, but just about every MK II turbo diesel I've seen that has the restrictor, got clogged at some point. Some NA's may have them too.
Since that hose is quite expensive (over $100), you can just drill out the restrictor and pull out the broken remains.
The Rabbit is about the same. I don't see that hose block too often, but it does happen from time to time. You can just replace the hose with something from NAPA or elsewhere.
Quick test to see if the overflow is clogged: Start the motor and leave the cap off. If you can't see coolant coming thru the overflow tube, assume it's blocked. THen you can take the hose off and try to blow backpressure through it with your mouth. If you can't then you need to address the hose.
If that's not the problem, then look to the thermostat.
I doubt that you blew the head gasket. You'd about have to pin the needle to blow the HG, and you said you stopped the car asap, so there likely is no damage there. But if you try to run it like this, there may be.
Good luck