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Since the discovery of ferroelectricity in HfO$_2$ thin films, significant research has focused on Zr-doped HfO$_2$ and solid solution (Hf,Zr)O$_2$ thin films. Functional properties can be further tuned via multilayering, however, this approach has not yet been fully explored in HfO$_2$-ZrO$_2$ films. This work demonstrates ferroelectricity in a 50 nm thick, solution-processed HfO$_2$-ZrO$_2$ multilayer film, marking it as the thickest multilayer film to date exhibiting ferroelectric properties. The multilayer structure was confirmed through transmission electron microscopy (TEM) and energy dispersive x-ray spectroscopy, with high-resolution TEM revealing grain continuity across multiple layers. This finding indicates that a polar phase in the originally paraelectric ZrO$_2$ layer, can be stabilized by the HfO$_2$ layer. The film attains a remanent polarization of 9 uC/cm$^2$ and exhibits accelerated wake-up behavior, attributed to its higher breakdown strength resulting from the incorporation of multiple interfaces. These results offer a faster wake-up mechanism for thick ferroelectric hafnia films.