Topology optimization is a well-established computational methodology for generating efficient structures with an excellent trade-off between material usage and performance. Recent advances in manufacturing technologies enable the fabrication of highly intricate optimized geometries, increasing the demand for topology optimization at fine-scale resolutions. Consequently, there is growing interest in developing computationally efficient methods for producing high-resolution optimized designs at reduced computational cost. In a recent study [1], a one-shot approach for minimum compliance topology optimization was investigated within the nested approach. For the convex problem of a variable thickness sheet (VTS) optimization, it was shown that an optimality criteria (OC) method employing only a single iteration of a multigrid-preconditioned conjugate gradient (MGCG) solver converges to the same solution as a fully accurate procedure. This behavior was attributed to the geometric multigrid preconditioner, which provides sufficiently accurate design sensitivities on a coarse scale. When applied to SIMP-based topology optimization, the one-shot approach yields layouts that capture the same primary load-carrying features as those obtained with accurate solvers. Preliminary results suggest that this strategy can be extended to more challenging functionals, such as stress. To gain deeper insight into the applicability of one-shot multigrid preconditioning, ongoing work is dedicated to the Simultaneous Analysis and Design (SAND) framework. Building on the multigrid-preconditioned primal-dual interior-point (IP) method with inexact linear solves [2], we explore the use of one-shot MGCG within the solution of the nonlinear KKT systems arising from VTS optimization. Numerical results reveal that a procedure with one Newton iteration per IP iteration, and one MGCG iteration per linear system, approaches the accurate solution as the step size for the barrier parameters is reduced – reproducing the success in the context of OC. The extension to the SAND formulation of SIMP-based topology optimization is not straightforward, but promising preliminary results will be presented and discussed.