We report on the feasibility of the direct measurement of the top Yukawa coupling g_t at the International Linear Collider (ILC) during its first phase of operation with a center-of-mass energy of 500 GeV. The signal and background models incorporate the non-relativistic QCD corrections which enhance the production cross section near the t-tbar threshold. The e+e- -> t tbar H signal is reconstructed in the 6-jet + lepton and the 8-jet modes. The results from the two channels are combined. The background processes considered are e+e- -> t bbar W- / tbar b W+ (which includes e+e- -> t tbar), e+e- -> t tbar Z, and e+e- -> t tbar g* -> t tbar b bar. We use a realistic fast Monte-Carlo detector simulation. Signal events are selected using event shape variables, through jet clustering, and by identifying heavy flavor jets. Assuming a Higgs mass of 120 GeV, polarized electron and positron beams with (Pe-,Pe+) = (-0.8,+0.3), and an integrated luminosity of 1 ab-1, we estimate that the e+e- -> t tbar H events can be seen with a statistical significance of 5.2 sigma, corresponding to the relative top Yukawa coupling measurement accuracy of |Delta g_t / g_t| = 10%.