We report on the imaging of the in situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane, finding excellent agreement with the scaling dynamics predicted by the Schrödinger equation. Our measurement provides a direct and quantitative observation of the textbook free expansion of a one-particle Gaussian wave packet, which we believe has no equivalent in the existing literature. Second, we utilize these expanding wave packets as a benchmark to develop a protocol for the controlled projection of a spatially extended wave function from continuous space onto the sites of a deep optical lattice and subsequent single-atom imaging using quantum gas microscopy techniques. By probing the square modulus of the wave function for various lattice ramp-up times, we show how to obtain a near-perfect projection onto lattice sites. Establishing this protocol represents a crucial prerequisite to the realization of a quantum gas microscope for continuum physics. The method demonstrated here for imaging a wave packet whose initial extent greatly exceeds the pinning lattice spacing, is designed to be applicable to the many-body wave function of interacting systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances.