Before revision:  If the protein explores the native-like states for a time much longer than the time to overcome the free energy barrier,  the resulting FPT distribution may be approximately single-exponential, as is expected for two-state folders, but the mean FPT (MFPT) to reach the native state will be determined by the time to find the native state among the native-like ones. The Kramers rate formula to estimate the transition times from the unfolded to the native-like states shows that these times are in reasonable agreement with the corresponding times obtained in the simulations and may be far shorter than the MFPTs to reach the native state  .
After revision:  If the protein explores the native-like states for a time much longer than the time to overcome the free energy barrier, the resulting FPT distribution may be approximately single-exponential, as is expected for two-state folders, but the mean FPT (MFPT) to reach the native state will be determined by the time to find the native state among the native-like states. The mean time to overcome the free energy barrier is found to be in reasonable agreement with the corresponding times obtained in the simulations and may be far shorter than the MFPTs to reach the native state .