C

$\because$抛物线$y=\left(x-3\right)^{2}$的顶点坐标为$\left(3,0\right)$，原点坐标为$\left(0,0\right)$，
$\therefore$将$\left(3,0\right)$左平移$3$个单位得到$\left(0,0\right)$，
故平移过程为：向左平移$3$个单位长度.
故选：$C$.