Advances in synthesis techniques and materials understanding have given rise to oxide heterostructures with intriguing physical phenomena that cannot be found in their constituents. In these structures, precise control of interface quality, including oxygen stoichiometry, is critical for unambiguous tailoring of the interfacial properties, with deposition of the first monolayer being the most important step in shaping a well-defined functional interface. Here, we studied interface formation and strain evolution during the initial growth of LaAlO3 on SrTiO3 by pulsed laser deposition, in search of a means for controlling the atomic-sharpness of the interfaces. Our experimental results show that growth of LaAlO3 at a high oxygen pressure dramatically enhances interface abruptness. As a consequence, the critical thickness for strain relaxation was increased, facilitating coherent epitaxy of perovskite oxides. This provides a clear understanding of the role of oxygen pressure during the interface formation, and enables the synthesis of oxide heterostructures with chemically-sharper interfaces. ; Comment: 25 pages