<p>Power distribution systems are increasingly challenged by extreme events that can significantly disrupt their operational performance and service continuity. Existing resilience quantification approaches largely rely on performance-based metrics and often overlook time-coupled resource adequacy during restoration. This paper proposes a system-driven, multi-dimensional resilience quantification methodology embedded within a two-stage power and energy restoration algorithm for distributed energy resource (DER)-rich distribution systems. Resilience here is quantified using a time-dependent metric that captures system performance degradation and recovery, incorporating load restoration and DER availability during the restoration process. Inverter-based (IB) DERs provide flexibility for restoring critical loads (CL); however, their time- and weather-dependent availability and diverse operating modes must be explicitly considered over the restoration horizon. To address this, a two-stage optimization framework is developed for resilience-driven system restoration, incorporating load prioritization based on event duration, impact severity, and resource constraints. The first stage uses penalty-based constraint handling to solve the non-linear optimization problem and restore maximum CLs through optimal network reconfiguration, while explicitly considering DER operational characteristics and control modes. The second stage optimizes power and energy beyond CLs, considering DER connectivity and resource management at different time steps. It further enhances restoration by incorporating real-time DER availability, capacity limits, and repair dynamics to ensure sustained recovery. Voltage-responsive loads are modeled for balanced IEEE-33 and unbalanced 123-bus systems, addressing the non-linear multi-constraint power flow optimization. The results demonstrate improved load restoration performance, effective utilization of DERs, and enhanced system resilience under diverse outage scenarios.</p>