The structural, thermodynamic, and kinetic aspects of the transformations between the metastable amorphous and crystalline phases of GaSb are investigated as a function of pressure at ambient temperature using synchrotron x-ray diffraction experiments in a diamond anvil cell. The results are consistent with the hypothesis that the pressure induced crystallization of amorphous GaSb into the β-Sn crystal structure near ~5 GPa is possibly a manifestation of an underlying polyamorphic phase transition between a semiconducting, low density and a metallic, high density amorphous (LDA and HDA, respectively) phases. In this scenario, the large differences in the thermal crystallization kinetics between amorphous GaSb deposited in thin film form by sputtering and that prepared by laser melt quenching may be related to the relative location of the glass transition temperature of the latter in the pressure-temperature (P-T) space with respect to the location of the critical point that terminate the LDA ↔ HDA transition. The amorphous → β-Sn phase transition is found to be hysteretically reversible as the β-Sn phase undergoes decompressive amorphization near ~2 GPa due to the lattice instabilities that give rise to density fluctuations in the crystal upon decompression.