if it's stone cold, then you start it and within a minute or two it starts to force water out of the engine then it's not going to be the cooling. ( it won't have got hot enough in that short time. )
it will be
1) cylinder head gasket leak.
2) cylinderhead cracked.(or distorted, not flat. )
3) cylinder bore cracked.
as you will have seen, these all will allow the high pressure fron the combustion chamber to escape into the relatively low presure area of the cooling system. resulting in loads of gasses bubbling up through the radiator / overflow.