Recently superconductivity and topological charge-density wave (CDW) were discovered in the Kagome metals $A$V$_3$Sb$_5$ ($A$ = Cs, Rb, and K), which have an ideal Kagome lattice of vanadium. Here we report resistance measurements on thin flakes of CsV$_3$Sb$_5$ to investigate the evolution of superconductivity and CDW with sample thickness. The CDW transition temperature ${it T}_{rm CDW}$ decreases from 94 K in bulk to a minimum of 82 K at thickness of 60 nm, then increases to 120 K as the thickness is reduced further to 4.8 nm (about five monolayers). Since the CDW order in CsV$_3$Sb$_5$ is quite three-dimensional (3D) in the bulk sample, the non-monotonic evolution of ${it T}_{rm CDW}$ with reducing sample thickness can be explained by a 3D to 2D crossover around 60 nm. Strikingly, the superconducting transition temperature ${it T}_{rm c}$ shows an exactly opposite evolution, increasing from 3.64 K in the bulk to a maximum of 4.28 K at thickness of 60 nm, then decreasing to 0.76 K at 4.8 nm. Such exactly opposite evolutions provide strong evidence for competing superconductivity and CDW, which helps us to understand these exotic phases in $A$V$_3$Sb$_5$ Kagome metals.
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