The automotive industry faces increasing pressure to accelerate vehicle design and production while adhering to stringent industry regulations. This process relies heavily on resource-intensive Computer-Aided Engineering (CAE) software, such as LS-Dyna, Ansys, and Abaqus, which require substantial computational power and costly, limited-availability software licenses. Priced based on the number of CPU cores utilized, these licenses can become a critical bottleneck, causing job delays, increased costs, and missed deadlines. To address limited computational resources, hybrid cloud infrastructures—integrating public cloud resources with on-premise High-Performance Computing (HPC) clusters—have emerged as a promising solution for scalable CAE job execution. However, while hybrid environments alleviate hardware constraints, they do not resolve software license limitations, which remain a significant hurdle to efficient job scheduling. Effectively leveraging hybrid infrastructures thus requires intelligent scheduling strategies that account for both compute and license constraints—an aspect largely overlooked in existing literature. In this paper, we propose License-Aware Deadline Miss Minimization Backfilling (LADMM_backfill), a novel scheduling algorithm designed to minimize deadline violations for CAE jobs under both license and compute resource constraints across hybrid cloud infrastructures. Our approach extends the traditional EASY backfilling algorithm by integrating real-time license availability into scheduling decisions and introducing dynamic heuristics to prioritize jobs for backfilling. This ensures efficient license utilization while maintaining strict compliance with licensing limits, preventing underutilization and overcommitment. Experimental evaluations show that LADMM_backfill improves license utilization by up to 94%, reduces deadline misses by 80%, average wait time by 97%, and makespan by 42% compared to established baselines, all while maintaining cost parity with conventional public cloud strategies. By balancing on-premise and cloud resources while respecting license constraints, LADMM_backfill offers a scalable and efficient solution for CAE job scheduling in hybrid cloud environments.