I don't know from experience, but I watched a bit from the making of The Nightmare Before Christmas, and they either poured or injected it into the mould when the two halves were already put together, so they filled it all the way. They had the mould standing up so it could be poured in an opening in the top.
The short movie on the making of that film was quite informative in that it followed puppet-making from conception all the way to finishing and animating through the various departments.