  We experimentally investigate charge transport through a single planar
junction between a NiTe$_2$ Dirac semimetal and a normal gold lead. At
millikelvin temperatures we observe non-Ohmic $dV/dI(V)$ behavior resembling
Andreev reflection at a superconductor -- normal metal interface, while
NiTe$_2$ bulk remains non-superconducting. The conclusion on superconductivity
is also supported by suppression of the effect by temperature and magnetic
field. In analogy with the known results for Cd$_3$As$_2$ Dirac semimetal, we
connect this behavior with interfacial superconductivity due to the flat-band
formation at the Au-NiTe$_2$ interface. Since the flat-band and topological
surface states are closely connected, the claim on the flat-band-induced
superconductivity is also supported by the Josephson current through the
topological surface states on the pristine NiTe$_2$ surface. We demonstrate the
pronounced Josephson diode effect, which results from the momentum shift of
topological surface states of NiTe$_2$ under an in-plane magnetic field.
