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We present an approach to approximating static properties of glasses without experimental inputs rooted in the first-principles random structure sampling. In our approach, the glassy system is represented by a collection (composite) of periodic, small-cell (few 10 s of atoms) local minima on the potential energy surface. These are obtained by generating a set of periodic structures with random lattice parameters and random atomic positions, which are then relaxed to their closest local minima on the potential energy surface using the first-principles methods. Using vitreous SiO2 as an example, we illustrate and discuss how well various atomic and electronic structure properties calculated as averages over the set of such local minima reproduce experimental data. The practical benefit of our approach, which can be rigorously thought of as representing an infinitely quickly quenched liquid, is in that it transfers the computational burden to linear scaling and easy to converge averages of properties computed on small-cell structures, rather than simulation cells with 100 s if not 1000 s of atoms while retaining a good overall predictive accuracy. Because of this, it enables the future use of high-cost/high-accuracy electronic structure methods, thereby bringing the modeling of glasses and amorphous phases closer to the state of modeling of crystalline solids.