A Si 2p core-level spectroscopic study has been performed in real time for initial thermal oxide on Si(100) by O-2 gas. Time evolutions of the intensities of chemically shifted Si 2p peaks during oxidation have been compared with those of O 2p state, as well as with a simulation from a set of rate equations assuming a simple oxidation model. From the best fits to the data, rate constants relevant to the oxidation of the first and the second silicon layers were successfully derived as a function of the oxidation temperature. In particular, the oxidation of the first layer for temperatures of 540-620 degrees C was found to occur through direct oxidation of silicon atoms to stoichiometric silicon dioxide, without formation of any suboxides.