We propose a temporally shaped double-picosecond-pulse train at a sub-nanosecond scale to control the damage dynamics of optical glass. Both damage threshold and morphology are significantly modulated by pulse-train shaping. The ramp-up-shaped train effectively increases its damage threshold and decreases the damage density and size, which clearly shows that a pump pulse with optimized fluence has a strong positive modification of damage precursors. Furthermore, the temporal evolution of damage modulation is experimentally revealed by varying the interval of pump-probe pulses, and after pump exposure with optimized fluence, enhancement of the probe threshold reaches the maximum at a delay of about 260 ps.