To quickly estimate tsunami hazards along the coastline, we present a data-driven transfer function method to reconstruct onshore tsunami hazard curves from offshore hazard curves with corresponding topographic and bathymetric data. The transfer function is approximated by a type of artificial neural network called a Variational Autoencoder (VAE). The VAE first encodes input data, including offshore hazard curves and topographic and bathymetric data. Once encoded, the data is represented by a normal distribution of latent variables. The VAE then uses a decoder that is trained to sample the distribution created by the latent variables and reconstruct a continuous hazard function at the onshore location. As the encoded values are represented by a probabilistic distribution, the resulting hazard curve output has inherent stochasticity. Thus, model variance can be found through many realizations of the transfer function for a single set of inputs. We developed a set of transfer functions to accurately predict the onshore hazard curves for (1) onshore flow depth, (2) Froude number (dimensionless velocity), and (3) dimensionless momentum flux. We construct two flow depth transfer functions, with one version utilizing an "anchor point" taken from established site-specific numerical modeling data. The VAEs to predict velocity and momentum flux incorporate an approach that leverages condensed topographic information around the point of interest (topographic rings). Overall, the transfer function method efficiently estimates onshore tsunami hazard curves, together with model uncertainty quantification, without requiring computationally expensive numerical simulations. The data and scripts used in this project are free to be re-used. under an MIT license.