The classical notion of time as a fundamental, continuous, and linear parameter is increasingly challenged by persistent puzzles in cosmology and quantum gravity. This paper proposes a paradigm shift by defining time not as a primary dimension, but as an emergent property of the evolution of spacetime's fractal structure. We introduce a novel framework where the flow of time is governed by the rate of change of the fractal dimension D, postulating a fundamental relation dt=dD/V(D), where V(D) is a fractal potential energy density. This core axiom naturally gives rise to a thermodynamic arrow of time and provides a singularity-free initial condition for the universe. Applying this model to cosmology, we derive a modified Friedmann equation and show that the observed age of the universe (13.8 Gyr) is consistently recovered through the calibration of V(D). Furthermore, the model offers first-principle explanations for late-time cosmic acceleration, interpreting dark energy as a manifestation of the fractal geometry's scale-dependence, and predicts a specific effective equation of state (w_eff=-1+p/3). At quantum scales, the framework predicts critical slowing down of particle interactions near specific fractal thresholds, potentially testable in high-energy experiments. Finally, we present a set of definitive, testable predictions, including specific imprints on the low-ℓ CMB power spectrum, anomalies in atomic clock comparisons, and deviations in the Hubble parameter measured from standard sirens. This work establishes fractal time as a viable and falsifiable hypothesis that bridges cosmological and quantum phenomena, offering a new path toward unifying gravity with the standard model.