Does our current understanding of the mass of black hole only allow for it to be located at the singularity?
As a star or neutron star collapses to form a blackhole there will, of course, be a moment when the matter is distributed everywhere within the event horizon.  So, there may not be a singularity within a full fledged blackhole, at first.  But, the inward forces within the event horizon are irresistible (considering that escape velocity is greater than the speed of light) and so everything within the event horizon must fall into a singularity.  How long this takes is complicated by the issue of which reference frame you chose to time it.