Controlled processing of transparent materials with ultrashort laser pulses requires a detailed and precise knowledge of the various laser-matter interaction mechanisms from laser energy deposition and conversion in internal energy of the material to hydrodynamic relaxation and mechanical response. To address this issue, we first develop a multi-timescale experimental approach based on a femtosecond pump-and-probe microscope-polariscope. The pump is a 360-fs, 1-μJ infrared (1030 nm) laser pulse which is split to provide a 515-nm femtosecond probe with delay adjustable from femtoseconds to nanoseconds. The obtained time-resolved shadowgraphy images allow measurement of the transient probe transmission. Then, the carrier density is determined by use of the Beer-Lambert law and Drude model approach demonstrating the ultrafast formation of a slightly overcritical plasma inside the bulk of fused silica. In parallel, quantitative birefringence images provide a measurement of stress by use of the photoelastic law revealing the partial dissipation of the absorbed laser energy through emission of a GPa-stress wave, a few hundreds of picoseconds after the laser pulse. A multiscale-multiphysics model is then used to interpret the experimental observations, accounting for the electron dynamics, laser propagation and the hydrodynamic response. Following experimental validation, simulations allow determining the temporal evolution of local fundamental material properties (stress, density and temperature). This combination of experimental and simulation results enables us to quantitatively discuss the importance of the different laser energy relaxation channels in the material uncovering the full scenario of the interaction. Our model predicts a 20-GPa maximum initial stress loading with maximum lattice temperatures reaching 3.5 10$^4$ K. We also show that a fraction of ~2% of the total absorbed laser energy is dissipated through emission of a weak shockwave. Our approach could be used in the future to account for mechanically-driven transparent material structuring induced by ultrashort laser pulses.