This paper introduces a new initialization scheme for enumerative algorithms in the Job Shop Scheduling Problem (JSSP). JSSP is a well-known NP-hard optimization problem that models one of the most general forms of manufacturing systems and has been extensively studied in the field of operations research. The proposed method, named Relative-Urgency Based Initialization (RUBI), improves the search efficiency of evolutionary algorithms for makespan optimization. The foundation of our approach is the Relative-Urgency (RU) principle, which theoretically aims to minimize the lower bound of the makespan. To quantify how well a JSSP solution aligns with this principle, we introduce the RU score—a metric that measures the degree to which the solution follows the RU principle. Empirical analysis reveals a strong correlation between the RU score and makespan. Based on this, we demonstrate that RUBI effectively guides the search process toward sub-optimal regions that are closer to the global optimum. Experimental results show that RUBI consistently improves the performance of the standard Genetic Algorithm (GA), both in terms of solution quality and time to reach the optimum. These findings suggest that the RU principle can contribute to the development of more efficient heuristics and frameworks for solving JSSP.