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We demonstrate that kinetics play an important role in the epitaxial growth of Fe$_3$GeTe$_2$ (FGT) van der Waals (vdW) ferromagnetic films by molecular beam epitaxy. By varying the deposition rate, we control the formation or suppression of an initial tellurium-deficient non-van der Waals phase (Fe$_3$Ge$_2$) prior to realizing epitaxial growth of the vdW FGT phase. Using cross-sectional scanning transmission electron microscopy and scanning tunneling microscopy, we optimize the FGT films to have atomically smooth surfaces and abrupt interfaces with the Ge(111) substrate. The magnetic properties of our high quality material are confirmed through magneto-optic, magnetotransport, and spin-polarized STM studies. Importantly, this demonstrates how the interplay of energetics and kinetics can help tune the re-evaporation rate of chalcogen atoms and interdiffusion from the underlayer, which paves the way for future studies of van der Waals epitaxy.