This talk focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the pseudo-stress variable is motivated by applications in non-Newtonian fluids and interface problems, where the stress field plays a central role in the physical description. The space-time discretisation of the problem is obtained by combining the PolyDG approach in space with the implicit Euler method in time, leading at each step to a symmetric and positive definite linear system whose conditioning deteriorates as the time-step size dt decreases. Numerical results indicate that standard iterative solvers, including common Krylov methods and basic block preconditioners, show a significant deterioration in convergence as dt decreases, a behaviour directly linked to the conditioning of the system matrix, which scales as 1/dt. To address this issue, we investigate two strategies tailored to the structure of the fully discrete system: (i) deflated Conjugate Gradient, which mitigates the influence of the most problematic eigenmodes, and (ii) a collective Block-Jacobi preconditioner which exploits the block structure induced by the pseudo-stress formulation. Numerical tests show that these approaches achieve iteration counts independent of dt, demonstrating robustness with respect to the time step. Overall, the talk highlights the proposed solvers as a robust framework for PolyDG discretisations on general polytopal meshes, while outlining ongoing research on multigrid strategies and theoretical analysis.