  Here, by conducting a systematic $^{89}$Y NMR study, we explore the nature of
the magnetic ground state in a newly discovered iron-based superconductor
YFe$_2$Ge$_2$. An incoherent-to-coherent crossover due to the Hund's coupling
induced electronic correlation is revealed below the crossover temperature
$T^*\sim 75\pm15\,\mathrm{K}$. During the electronic crossover, both the Knight
shift ($K$) and the bulk magnetic susceptibility ($\chi$) exhibit a similar
nonmonotonic temperature dependence, and a so-called Knight shift anomaly is
also revealed by a careful $K$-$\chi$ analysis. Such an electronic crossover
has been also observed in heavily hole-doped pnictide superconductors
\emph{A}Fe$_2$As$_2$ (\emph{A} = K, Rb, and Cs), which is ascribed to the
Hund's coupling induced electronic correlation. Below $T^*$, the spin-lattice
relaxation rate divided by temperature $(1/T_1T)$ shows a similar suppression
as the Knight shift, suggesting the absence of critical spin fluctuations. This
seems to be in conflict with a predicted magnetic quantum critical point (QCP)
near this system. However, considering a $\mathbf{q}$-dependent "filter" effect
on the transferred hyperfine field, a predominant spin fluctuation with A-type
correlation would be perfectly filtered out at $^{89}$Y sites, which is
consistent with the recent inelastic neutron scattering results. Therefore, our
results confirm that, through a Hund's coupling induced electronic crossover,
the magnetic ground state of YFe$_2$Ge$_2$ becomes close to an itinerant
magnetic QCP with A-type spin fluctuations. In addition, the possible
superconducting pairing due to spin fluctuations is also discussed.
