There are a lot of problems with the conventional fusion welding process, so ultrasonic welding has been used for about 20 years and has helped a lot of manufacturing industries, including aviation, medicine, and microelectronics. Ultrasonic welding takes less than one second, making it suitable for mass production. Poor weld quality and joint strength are common issues that industries encounter as a result of this process. Actually, the success and quality of the welding are determined by its control parameters. This research examines the impacts of weld time, vibrational amplitude, and weld pressure on the welding of 0.6 mm thick sheets of two different metals, specifically copper and aluminum (AA2024). Responses, including tensile shear stress, weld area, and T-peel stress, are acquired through experiments that follow a full factorial design including four replicas. The highest recorded tensile shear stress was 4.34 MPa, the maximum weld area measured was 63.6 mm2, and the peak T-peel stress reached 1.22 MPa. A second-order non-linear regression model was constructed using all of these data points, which related the responses to the predictors. Due to the importance of quality in the production sector, the process parameters were determined by the combination of genetic algorithm (GA) and fuzzy logic (FL) approaches. The impact of the weld zone temperature on various quality characteristics has been investigated through experiments. It has been noted from the confirmatory test that FL produces superior output outcomes compared to the genetic algorithm, with FL achieving a fuzzy multi-performance index of 0.94 compared to 0.61 for GA. By conducting microstructural analysis, weld quality levels, including “under-weld,” “good weld,” and “over-weld,” were established.