Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under the simplifying assumption of a Gaussian distribution. We extend this framework by modeling inputs as Gaussian mixtures to better represent complex, real-world data. Through empirical and theoretical investigation, we demonstrate that with proper standardization, the learning dynamics converges to the behavior seen in the simple Gaussian case. This finding exhibits a form of universality, where diverse structured distributions yield results consistent with Gaussian assumptions, thereby strengthening the theoretical understanding of deep learning models.