We present the production of quantum degenerate, superfluid gases of 6Li through direct evaporative cooling in a cavity-enhanced optical dipole trap. The entire evaporative cooling process is performed in a trap created by the TEM00 mode of a Fabry-Pérot cavity, simultaneously driven on several successive longitudinal modes. This leads to near-complete cancellation of the inherent lattice structure along the axial direction of the cavity, as evidenced by the observation of long-lived dipole oscillations of the atomic cloud. We demonstrate the production of molecular Bose-Einstein condensates upon adiabatic conversion of a unitary Fermi gas evaporatively cooled in this trap. The lifetime and heating in the cavity trap are similar to those in a running wave dipole trap. Our system enables the optical production of ultracold samples using a total trap-laser power below 1 W, leveraging the benefits of optical resonators as dipole traps in quantum gas research while maintaining a simple resonator design and minimizing additional experimental complexity.