Modeling and research are done on an unsteady squeezing flow of Casson fluid traveling through a porous media channel with a magnetohydrodynamic (MHD) effect. The non-Newtonian fluid partial differential equations (PDEs) are similarity transformed into a highly nonlinear fourth-order ordinary differential equation (ODE). The resultant boundary value issue is resolved numerically using the Hermite wavelet method (HWM) and Differential transformation Method (DTM). We compare the numerical findings, which exhibit great agreement, for validity considerations. Additionally, a thorough visual study has been done to look at how different fluid factors affect the velocity, temperature, and concentration profile. Analysis reveals that the velocity profile is affected differently by positive and negative squeeze numbers. Moreover, it has been shown that when the squeeze number is positive or negative, the Casson parameter has the opposite influence on the velocity profile. In cases of positive and negative squeezing numbers, the MHD parameter and permeability constant have equivalent impacts on the velocity profile. Further, it can be shown that identical velocity profiles for Casson, MHD, and permeability parameters have been found in cases when the squeeze number is positive. In addition, a skin-friction coefficient study has also been provided. It has been found that the skin friction coefficient has an inverse connection with the Casson parameter whereas the squeeze number, MHD parameter, and permeability parameter all have direct relationships. The effect of several relevant factors on the temperature and concentration fields is also addressed, with the use of graphical examples.