We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well described by the superfluid regime of the Bose-Hubbard model, which allows for comparison with mean-field theories and exact quantum Monte Carlo (QMC) simulations. By correcting for systematic discrepancies between condensate and peak fraction, we find that the QMC simulations and measured peak fraction agree at low entropies per particle. At high entropy, however, we discover that the experiment consistently shows the presence of a condensate at temperatures higher than the critical temperature predicted by QMC simulations. This metastability suggests that turning on the lattice potential is nonadiabatic. To confirm this behavior, we compute the time scales for relaxation in this system, and find that equilibration times are comparable with the known heating rates. The similarity of these time scales implies that turning on the lattice potential adiabatically may be impossible. Our results point to the urgent need for a better theoretical and experimental understanding of the time scales for relaxation and adiabaticity in strongly interacting quantum gases, and the importance of model-independent probes of thermometry in optical lattices.