The short answer is no, the neutron degeneracy pressure for a neutron star of mass greater than around 2.16 time the mass of our sun (Tolman–Oppenheimer–Volkoff limit) is insufficient to stop it collapsing.

This is well below the mass density where an even horizon would form, thus a neutron star cannot simultaneously be a black hole.

If though there were a state of matter at higher density than neutron matter (perhaps a quark plasma or quark stranglet) that could stabilize the collapse before the critical radius is reached then there may be something denser than a neutron star. But this would not be a black hole.

But according to our current understanding of science, once the collapsing sphere is denser than the the Schwarzschild radius an even horizon forms & within that radius no known state of matter is sufficient to withstand it ultimately forming a singularity.

It would be very difficult with a non-rotating black hole to prove otherwise anyway as the event horizon forms an information boundary to external observers & also for infalling instrumentation.