Does our current understanding of the mass of black hole only allow for it to be located at the singularity? Does the distribution of mass or density of mass inside the event horizon matter for a black hole to exist as we currently theorize? Could the mass inside the event horizon be distributed in any way at all, or have any density so long as it is dense enough to locate 100% of the mass inside the Schwarzschild radius?
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.