Invariant manifolds, in general, and Spectral Submanifolds (SSM), in particular, have emerged as rigorous and predictive model reduction tools for nonlinear dynamical systems. Recent developments have enabled direct computation of invariant manifolds and their reduced dynamics for high-dimensional finite-element (FE) models by solving the associated invariance equations in physical coordinates using only the eigenvectors associated with the master modal subspace. However, FE models in commercial solvers generally do not provide information on the nonlinearities required for the direct approximation of invariant manifolds. In this talk, we show how to overcome this limitation using a nonintrusive construction of invariant manifolds and their reduced dynamics in a data-free environment. We also show how SSM-based ROMs are useful in extracting physical relevant information such as the forced response curves in nonlinear mechanical systems without performing any costly forced simulations. We include demonstrations over nonlinear systems ranging from simple structures, such as beams and shells, to more complex geometries, such as a MEMS device containing more than a million degrees of freedom.