Matter-wave interference is a cornerstone of quantum mechanics. It not only provides a rigorous test of wave-particle duality and the quantum superposition principle but also underpins the manipulation of quantum states in cutting-edge technologies like quantum computing and quantum sensing. We report an approach to directly generate and observe double-slit interference of matter waves at the single-particle level. This method circumvents the limitations inherent in traditional ensemble-based experiments—for instance, those employing Bose-Einstein condensates—which probe only ensemble-averaged behavior and thus cannot reveal intrinsic single-particle quantum properties. We present a theoretical scheme and an experimental framework designed to enable the direct verification of wave-particle duality and quantum superposition for individual particles on an optical lattice platform. Our approach employs a two-color, one-dimensional optical lattice to coherently split the matter-wave packet of a single trapped strontium atom. This is accomplished by adiabatically converting a single harmonic potential into two spatially separated wells. After releasing the potential, the two wave packets freely expand and interfere. We simulate this entire process—from adiabatic splitting to free-space interference—by numerically solving the time-dependent Schrödinger equation. Our analysis focuses on the effect of adiabatic evolution time on fringe quality, optimizes the adiabatic trajectory using the inverse-square dependence on the energy gap, and evaluates how initial thermal noise degrades fringe contrast. Benchmarked against a linear adiabatic path, our optimized scheme delivers higher ground-state fidelity within a significantly reduced evolution time, thereby improving robustness against environmental noise. Numerical simulations confirm that initial thermal noise substantially degrades the contrast of the interference fringes. A feasibility analysis for strontium atoms demonstrates that the requisite cooling performance, experimental timescales, and imaging resolution are all within reach of established techniques. This study presents a theoretical scheme and a experimental framework for directly probing matter-wave interference at the single-particle level. It clarifies the role of key parameters and provides concrete guidance for future experiments in this direction.