For the first time within a multi-angle computational framework we investigate the time evolution of neutrino halo effects on collective neutrino oscillation (CNO) in an iron core-collapse supernova. For the collapse of the 9.6M⊙ progenitor employed in this work, we find that there is a window of time where one can safely calculate CNO including the neutrino halo effects due to the density gradient of the envelope. The impact of inward-scattered neutrino flux on CNO can not be ignored inside the shock front, compared with the outward-propagating neutrino flux. However, there is a window of time where CNO is not shut down by multi-angle matter suppression and delayed in onset beyond the radius of the growing shock front. Halo neutrinos with wider intersection trajectories induce a delay for the onset radius of CNO, while they produce additional flavor conversion for neutrino spectra. This additional flavor conversion sharpens CNO spectral features, leading to a detected neutrino signal which is more clearly distinguishable from thermal emission than when halo neutrinos are omitted.