This paper investigates the combination of parametric channel estimation with minimum mean square error (MMSE) estimation. We propose a two-stage channel estimation technique that utilizes the decomposition of wireless communication channels into a distinct line-of-sight (LoS) path and multiple reflected scattered clusters. Firstly, a direction-of-arrival (DoA)-based estimator is formulated to estimate the LoS component. Afterwards, we utilize a Gaussian mixture model to estimate the conditionally Gaussian distributed random vector, which represents the multipath propagation. The proposed two-stage estimator allows pre-computing the respective estimation filters, tremendously reducing the computational complexity. Numerical simulations with typical channel models depict the superior performance of our proposed two-stage estimation approach as compared to state-of-the-art methods.