We study the very early light curve of supernova 2014J (SN 2014J) using the high-cadence broad-band imaging data obtained by the Kilodegree Extremely Little Telescope, which fortuitously observed M 82 around the time of the explosion, starting more than 2 months prior to detection, with up to 20 observations per night. These observations are complemented by observations in two narrow-band filters used in an H alpha survey of nearby galaxies by the intermediate Palomar Transient Factory that also captured the first days of the brightening of the supernova. The evolution of the light curves is consistent with the expected signal from the cooling of shock heated material of large scale dimensions, > ~1R sub(middot in circle). This could be due to heated material of the progenitor, a companion star or pre-existing circumstellar environment, e.g., in the form of an accretion disk. Structure seen in the light curves during the first days after explosion could also originate from radioactive material in the outer parts of an exploding white dwarf, as suggested from the early detection of gamma-rays. The model degeneracy translates into a systematic uncertainty of + or -0.3 days on the estimate of the first light from SN 2014J.