In this article it is argued that a continuity exists between Karl Schwarzschild's work on foundational problems on the borderline of physics and astronomy and his later occupation with general relativity. Based on an analysis of Schwarzschild's published works as well as formerly neglected unpublished notes it is shown that, long before the rise of general relativity, Schwarzschild was concerned with problems that later became associated with that theory. In particular he considered non-Euclidean cosmologies, linked the phenomena of gravitation and inertia to the problem of the precession of Mercury's perihelion, and entertained the possibility of inertial frames rotating with respect to one another. It is argued that these earlier considerations, which reflect his interdisciplinary outlook on the foundations of the exact sciences, enabled Schwarzschild to recognize the significance of general relativity for astronomy, astrophysics, and cosmology earlier than most of his collegues and shaped his contributions to this theory.