Let (Mn, g) be a compact n-dimensional (n >= 2) manifold with nonnegative Ricci curvature, and if n >= 3, then we assume that (Mn, g) × R has nonnegative isotropic curvature. The lower bound of the Ricci flow’s existence time on (Mn, g) is proved. This provides an alternative proof for the uniform lower bound of a family of closed Ricci flows’ maximal existence times, which was first prove…