This paper introduces a comprehensive framework for Post-Disaster Search and Rescue (PDSR), aiming to optimize search and rescue operations leveraging Unmanned Aerial Vehicles (UAVs). The primary goal is to improve the precision and availability of sensing capabilities, particularly in various catastrophic scenarios. Central to this concept is the rapid deployment of UAV swarms equipped with diverse sensing, communication, and intelligence capabilities, functioning as an integrated system that incorporates multiple technologies and approaches for efficient detection of individuals buried beneath rubble or debris following a disaster. Within this framework, we propose architectural solution and address associated challenges to ensure optimal performance in real-world disaster scenarios. The proposed framework aims to achieve complete coverage of damaged areas significantly faster than traditional methods using a multi-tier swarm architecture. Furthermore, integrating multi-modal sensing data with machine learning for data fusion could enhance detection accuracy, ensuring precise identification of survivors.