The dynamics of nonlinear optical processes in epsilon-near-zero (ENZ) transparent conductive oxides (TCOs) are primarily governed by hot electron relaxation with a sub-picosecond response. However, there is currently a lack of comprehensive understanding of the ultrafast electron dynamics in nonlinear TCO ENZ materials. This study investigates the effects of laser peak power and ENZ mode excitation on hot electron relaxation in TCOs. Our experimental analysis theoretically supported by a hydrodynamic model reveals that increasing laser pulse intensity extends hot electron relaxation time by more than 200%, while ENZ mode excitation increases it by more than 40% in representative TCO ENZ materials. This research demonstrates the controllable modulation of ultrafast ENZ nonlinearity via pulse peak power and ENZ mode field enhancement. These findings provide substantial insights into the potential utilization of ENZ nonlinearity for the development of optical and quantum computing components, including ultrafast optical switches, dynamic pulse shapers, and modulators.