We model the expansion history of the Universe as a Gaussian process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy and Lyman-alpha data sets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Joint Light-Curve Analysis sample, cosmic microwave background data from the Planck satellite, and local measurement of the Hubble parameter from the Hubble Space Telescope (H0). Our analysis shows that the cosmic microwave background, Luminous Red Galaxy, Lyman-alpha, and Joint Light-Curve Analysis data are consistent with each other and with a ΛCDM cosmology, but the H0 data are inconsistent at moderate significance. Including the presence of dark radiation does not alleviate the H0 tension in our analysis. While some of these results have been noted previously, the strength here lies in that we do not assume a particular cosmological model. We calculate the growth of the gravitational potential in General Relativity corresponding to these general expansion histories and show that they are well approximated by Ωm0.55 given the current precision. We assess the prospects for upcoming surveys to measure deviations from ΛCDM using this model-independent approach.