We study numerically the early stage domain coarsening dynamics of the temperature driven isotropic-nematic (I-N) liquid crystal phase transition. System of rod like objects which interact via the modified Lebwohl-Lasher pairwise interaction is considered in 3D. The coarsening dynamics is followed using Brownian molecular dynamics. The box-restricted lattice point fluctuations are allowed in order to get rid of lattice geometry enforced phenomena. We analyze order parameter growth and domain coarsening in the early regime of the I-N phase transition as a function of the quench rate. We show that soon after the transition bimodal distribution of domains appears, where the shorter branch gradually vanishes. The behavior of the system is in accordance with predictions of the Kibble-Zurek mechanism which was originally introduced to model conditions in the early universe.