We introduce a ghost finite element framework for the numerical simulation of time-dependent partial differential equations, with a particular focus on fluid flow problems. We employ a time-stepping scheme such as the Backward Differentiation Formulas (BDF) for temporal discretization and an unfitted ghost finite element method (FEM) for spatial discretization. The nonlinear term of the governing equations can lead to a loss in computational efficiency when solved directly. To address this, we linearize the nonlinear solver; however, this linearization introduces a loss in the overall accuracy of the method. To mitigate this issue and recover higher-order accuracy, we incorporate implicit-explicit (IMEX) schemes. We examine the numerical properties of the proposed method through a series of benchmark tests, assessing accuracy, stability, and convergence. The performance of the framework is validated against canonical fluid flow benchmarks, confirming its robustness. Furthermore, we present a scalable multigrid solver specifically tailored to this formulation. The Nitsche's technique is used for weak imposition of boundary conditions. The choice of the penalization parameter in Nitsche’s method plays a crucial role: it must be sufficiently large to guarantee the stability of the overall method, but not so large that it adversely impacts the performance of the multigrid solver. We present results to demonstrate that with appropriate tuning, the method achieves an effective balance between stability, accuracy, and computational efficiency.