This contribution bases on the established model for sea ice dynamics, which describes the viscous-plastic sea ice behavior at scales spanning several thousand kilometers, cf. [1]. Focus of the numerical model is on the simulation of the sea ice circulation and its evolution over a seasonal cycle. Therefore, it takes into account the sea ice thickness as well as the sea ice concentration. The physical behavior of the later two quantities are governed by transient advection equations, in which the sea ice velocity serves as coupling field. Recent investigations proposed the finite element implementation of the sea ice model based on a (mixed) Galerkin variational approach, see e.g. [2 and [3]. However, challenges arise in stabilizing the numerically complex scheme, particularly in dealing with the first-order advection equations. In order to address these challenges, the utilization of the mixed least-squares method is promising. One main advantage of this method is its applicability to first-order systems, i.e., it provides stable and robust formulations even for non-self-adjoint operators, such as the tracer equations (for sea ice thickness and sea ice concentration). The here presented least-squares finite element formulation bases on the instationary sea ice equation, including the balance of momentum and a constitutive law for the viscous-plastic flow. In the utilized mixed least-squares approach four primary fields are considered, which are the stress, the velocity, the concentration and the thickness. Four residuals are defined for the derivation of a first-order least-squares formulation based on the balance of momentum, the constitutive relation for the stresses, and two tracer-equations. In comparison to our previous investigations, a distinctive approach is proposed in which the stresses are approximated in a non-conforming manner. Hence, instead of employing H(div) conforming interpolation functions, Lagrange interpolation functions for the stresses are utilized aligning them with the interpolation approach used for other fields. These two approaches are compared analyzing a box test case, see [3], to validate the new approach. Moreover, the results are compared to existing literature.