  Thin films of $ \beta- $tungsten host superconductivity in the presence of
strong spin-orbit coupling. This non-equilibrium crystalline phase of tungsten
has attracted considerable attention in recent years due to its giant spin Hall
effect and the potential promise of exotic superconductivity. However, more
than 60 years after its discovery, superconductivity in this material is still
not well understood. Using time-domain THz spectroscopy, we measure the
frequency response of the complex optical conductivity of $ \beta- $tungsten
thin film with a T$_c$ of 3.7 K in its superconducting state. At temperatures
down to 1.6 K, we find that both the superconducting gap and the superfluid
spectral weight are much smaller than that expected for a weakly coupled
superconductor given the T$_c$. The conclusion of a small gap holds up even
when accounting for possible inhomogeneities in the system, which could come
from other crystalline forms of tungsten (that are not superconducting at these
temperatures) or surface states on $ \beta- $tungsten grains. Using detailed
X-ray diffraction measurements, we preclude the possibility of significant
amount of other tungsten allotropes, strongly suggesting the topological
surface states of $ \beta- $tungsten play the role of inhomogeneity in these
films. Our observations pose a challenge and opportunity for a theory of
strongly anisotropic normal metals with strong spin-orbit coupling to describe.
