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 Hunds coupling induced electronic correlation is revealed below the crossover temperature $T^*sim 75pm15,mathrm{K}$. 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 Hunds 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 Hunds 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.
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