Abstract We present high-cadence optical and ultraviolet light curves of the normal Type Ia supernova (SN) 2021aefx, which shows an early bump during the first two days of observation. This bump may be a signature of interaction between the exploding white dwarf and a nondegenerate binary companion, or it may be intrinsic to the white dwarf explosion mechanism. In the case of the former, the short duration of the bump implies a relatively compact main-sequence companion star, although this conclusion is viewing-angle dependent. Our best-fit companion-shocking and double-detonation models both overpredict the UV luminosity during the bump, and existing nickel-shell models do not match the strength and timescale of the bump. We also present nebular spectra of SN 2021aefx, which do not show the hydrogen or helium emission expected from a nondegenerate companion, as well as a radio nondetection that rules out all symbiotic progenitor systems and most accretion disk winds. Our analysis places strong but conflicting constraints on the progenitor of SN 2021aefx; no current model can explain all of our observations.