Numerically generating synthetic surface topography that closely resembles the features and characteristics of experimental surface topography measurements reduces the need to perform these intricate and costly measurements. However, existing algorithms to numerically generated surface topography are not well-suited to create the specific characteristics and geometric features of as-built surfaces that result from laser powder bed fusion (LPBF), such as partially melted metal particles, porosity, laser scan lines, and balling. Thus, we present a method to generate synthetic as-built LPBF surface topography maps using a progressively growing generative adversarial network. We qualitatively and quantitatively demonstrate good agreement between synthetic and experimental as-built LPBF surface topography maps using areal and deterministic surface topography parameters, radially averaged power spectral density, and material ratio curves. The ability to accurately generate synthetic as-built LPBF surface topography maps reduces the experimental burden of performing a large number of surface topography measurements. Furthermore, it facilitates combining experimental measurements with synthetic surface topography maps to create large data-sets that facilitate, e.g. relating as-built surface topography to LPBF process parameters, or implementing digital surface twins to monitor complex end-use LPBF parts, amongst other applications.