  In the new van der Waals Kondo-lattice Fe$_3$GeTe$_2$, itinerant
ferromagnetism and heavy fermionic behaviour coexist. Both the key properties
of such a system namely a spin-polarized Fermi surface and a low Fermi momentum
are expected to significantly alter Andreev reflection dominated transport at a
contact with a superconducting electrode, and display unconventional
proximity-induced superconductivity. We observed interplay between Andreev
reflection and Kondo resonance at mesoscopic interfaces between superconducting
Nb and Fe$_3$GeTe$_2$. Above the critical temperature ($T_c$) of Nb, the
recorded differential conductance ($dI/dV$) spectra display a robust zero-bias
anomaly which is described well by a characteristic Fano line shape arising
from Kondo resonance. Below $T_c$, the Fano line mixes with Andreev reflection
dominated $dI/dV$ leading to a dramatic, unconventional suppression of
conductance at zero bias. As a consequence, an analysis of the Andreev
reflection spectra within a spin-polarized model yields an anomalously large
spin-polarization which is not explained by the density of states of the
spin-split bands at the Fermi surface alone. The results open up the
possibilities of fascinating interplay between various quantum phenomena that
may potentially emerge at the mesoscopic superconducting interfaces involving
Kondo lattice systems hosting spin-polarized conduction electrons.
