Understanding the irregular variation of the solar cycle is crucial due to its significant impact on global climates and the heliosphere. Since the polar magnetic field determines the amplitude of the next solar cycle, variations in the polar field can lead to fluctuations in the solar cycle. We have explored the variability of the solar cycle at different levels of dynamo supercriticality. We observe that the variability depends on the dynamo operation regime, with the near-critical regime exhibiting more variability than the supercritical regime. Furthermore, we have explored the effects of the irregular BMR properties (emergence rate, latitude, tilt, and flux) on the polar field and the solar cycle. We find that they all produce considerable variation in the solar cycle; however, the variation due to the tilt scatter is the largest.