In physical terms, continuity refers to smooth change of something through time.
To go from nothing to something surely is a non-smooth event, a discontinuous change.
So if continuity is to be followed, we must have 'from nothing comes nothing'.
Also, can we say that continuity is a more basic principle, or at least on a par with nothing - as it can be used to establish its invariance in time.
Of course this is not a mathematical argument - and can't be understood rigourously.
More fundamentally, if one has nothing, then one also has no time either. So its a triviality that 'from nothing, nothing'. So in the argument should one allow at least both space and time?