The milling effects of a precursor $Y_2BaCuO_5$ (Y211) powder having 1 wt.% $CeO_2$ on the microstructure and critical current density ($J_c$) of liquid infiltration growth (LIG) processed $YBa_2Cu_3O_{7-y}$ (Y-123) bulk superconductors were investigated. The microstructure analysis revealed that the Y211 size in the final Y-123 products decreased with increasing the milling time and a relatively high density and uniform distribution of Y211 inclusions were observed in the sample prepared using 8 h milled powder. However, the unexpected Y211 particles coarsening was observed from the 4 h milled sample which was further increased for 10 h milled sample. Critical current density ($J_c$) of the LIG processed Y-123 bulk superconductors was found to be dependent on the milling time of the Y211 precursor powder. The $J_c$ increased with the increase of milling time and reached up to a maximum at 8 h in the self field while 10 h milled sample showed lower $J_c$ at the same field which might be due to the exaggerated growth and non-uniform distribution of Y211 particles.