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Cosmic Reionization imprints its signature on the temperature and polarization anisotropies of the cosmic microwave background (CMB). Advances in CMB telescopes have already placed a significant constraint on the history of reionization. As near-future CMB telescopes target the maximum sensitivity, or observations limited only by the cosmic variance (CV), we hereby forecast the potential of future CMB observations in constraining the history of reionization. In this study, we perform Markov Chain Monte Carlo analysis for CV-limited E-mode polarization observations such as the LiteBIRD (Light satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection), based on a few different methods that vary in the way of sampling reionization histories. We focus especially on estimating the very early history of reionization that occurs at redshifts $z>15$, which is quantified by the partial CMB optical depth due to free electrons at $z>15$, $τ_{z>15}$. We find that reionization with $τ_{z>15} \sim 0.008$, which are well below the current upper limit $τ_{z>15} \sim 0.02$, are achievable by reionization models with minihalo domination in the early phase and can be distinguished from those with $τ_{z>15} \lesssim 5\times 10^{-4}$ through CV-limited CMB polarization observations. An accurate estimation of $τ_{z>15}$, however, remains somewhat elusive. We investigate whether resampling the E-mode polarization data with limited spherical-harmonic modes may resolve this shortcoming.