Predicting the onset of fracture in soft viscoelastic materials remains a fundamental challenge, especially when damage initiates well before macroscopic crack propagation. Recent experimental work by Ju et al. [1] has revealed the presence of early-stage fracture precursors—localized molecular damage that triggers long-range strain-rate fields—well ahead of catastrophic failure. Capturing such phenomena within a predictive theoretical framework is essential for designing resilient materials and preventing unexpected failures. In this study, we present a thermodynamically consistent viscoelastic phase-field fracture model that is particularly well-suited to describe these early damage processes, building upon recent modeling approaches by Ciambella et al. [2]. The model distinguishes between equilibrium and non-equilibrium elastic energies and introduces two characteristic time scales to separately capture bulk viscoelastic relaxation and localized damage evolution near the crack tip. This dual-timescale formulation allows us to simulate the accumulation of subcritical damage and the associated mechanical fields observed in experiments. We demonstrate that our model can replicate key features of the delayed fracture dynamics reported by Ju et al. [1], including the emergence of long-range strain-rate fields in response to highly localized damage. This makes our approach a powerful tool not only for reproducing observed phenomena, but also for exploring how changes in material properties or loading conditions influence precursor activity.