Laser-induced damage growth on the exit surface of fused silica optics triggered by nanosecond pulses at 351 nm is widely described with exponential dynamics. In this Letter, a particular experimental setup allowed us to study damage growth with a large beam and fluences near damage growth threshold for a high number of shots. This allowed us to observe and characterize a regime with a slow and linear growth dynamic not documented in the literature and yet fundamental for the operation of high-power laser installations.