Intermittent river-groundwater connectivity can be a dynamic, transient process, but quantifying transition from disconnection to connection has focused mainly on steady-state behavior. To quantitatively evaluate the transient connection behavior, HYDRUS-2D was used to simulate the water flow beneath the lower Rio Grande riverbed in southern New Mexico during the beginning of dam water release. The river wave initially arrived in the channel center and later spread across the entire channel. The infiltration was monitored by shallow buried water content and pressure sensors. Transient and steady-state simulations were used to quantify the relationship between hydraulic head difference and the infiltration rate during transition to connection. Transient and steady state disconnection-connection transitions were both impacted by heterogeneity when evaluated with infiltration versus head difference. During surface water arrival, steady-state infiltration behavior only increased nonlinearly with head difference, whereas transient infiltration behavior increased and then decreased with increasing head difference. This revealed three piecewise linear trends oriented in a triangular shape including both increases and decreases of infiltration rates. Infiltration tends to be significantly underestimated at the beginning of surface water arrival, when using steady-state conditions rather than transient conditions. These findings have implications for informing management of ephemeral stream systems, which impacts water resources prediction and sustainable water management, especially in arid and semi-arid regions where intermittent streams and rivers are more common.