Material response and the launch of laser plasma during the 1064 nm nanosecond laser pulse induced damage to the exit surface of fused silica are investigated. Employing a polarization-based two-frame shadowgraphy setup with ～ 60 fs probing resolution, the transient material responses from the rising part of nanosecond pumping pulse to several hundred nanosecond timescale are captured. Using a shearing interferometry setup, the evolution of transient phase shift of laser plasma in the expansion process to the ambient air is also investigated. Inhomogeneous distribution of phase shift caused by the electrons and neutrals in the plasma is quantitatively resolved by employing the fast Fourier transform based filtering algorism. To demonstrate the evolutions of important plasma parameters such as pressure, temperature and density, a continuum hydrodynamic model is numerically solved. The initial pressure of plasma is estimated according to the point-explosion model, and the initial plasma temperature is achieved by calculating the difference between simulating shockwave front radius and experimental value at the same delay. The optimal temperature is chosen when the radius difference is minimal. Main conclusions are as follows. 1) Abundant suprathermal electrons are excited in the early energy deposition process. Part of these electrons contribute to the thermal transport process and produce the laser supported solid-state absorption front (LSSAF) which propagates into the bulk silica. Other electrons escape to the air side and contribute to the formation of air plasma through the impact ionization process. Plasma expansion speed is about 20 km/s during this phase. 2) When the pump pulse is terminated, the LSSAF and air plasma lose their energy supplied and experience a rapid decline of the temperature and expansion velocity. As a result, the final damage crater depth exhibits seldomly no increase compared with the transient crater depth during this phase. Hot bulk plasma formed in this phase becomes the damage precursor and induces the ejection of abundant neutrals probably due to the phase explosion mechanism. Inhomogeneous distribution of stress is formed by Rayleigh-Taylor instability at the interface between hot bulk plasma and surrounding bulk material during the expansion of LSSAF. Radial and circumferential cracks are formed due to the release of stress. 3) Evolution of air plasma follows the conventional evolution process of laser-induced plasma, i. e. , internal pressure, temperature and density decrease quickly with time delay. The simulated transient highest pressure is about 600 MPa. Simulation also predicts the formation of the internal shockwave. Our work will be helpful in understanding the laser damage mechanism of the fused silica optical window.